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Computer input/output: adams_7.17.part1.out
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jda@Leonidas:~/atlasSoftware/master/atlasofliegroups/atlas-scripts$ ../atlas all
This is 'atlas' (version 1.0.6, axis language version 0.9.5),
the Atlas of Lie Groups and Representations interpreter,
compiled on Jul 10 2017 at 11:13:00. http://www.liegroups.org/
atlas>
atlas>
atlas> set G=SO(4,4)
Variable G: RealForm
atlas> G
Value: disconnected split real group with Lie algebra 'so(4,4)'
atlas> simple_roots (G)
Value:
| 1, 0, 0, 0 |
| -1, 1, 0, 0 |
| 0, -1, 1, 1 |
| 0, 0, -1, 1 |
atlas> components_rank (G)
Value: 1
atlas> set G=Spin(4,4)
Variable G: RealForm (overriding previous instance, which had type RealForm)
atlas> G
Value: connected split real group with Lie algebra 'so(4,4)'
atlas> print_Z(G)
Group is semisimple
center=Z/2Z x Z/2Z
atlas> set K=K_0(KGB(G,0))
Variable K: RealForm
atlas>
atlas> K
Value: compact connected real group with Lie algebra 'su(2).su(2).su(2).su(2)'
atlas>
atlas> set special(Param p, int height)=void:
: > let br=branch_irreducible(p,height) in
I > for p in monomials(br) do let mu=highest_weight(LKT(p)) in let (x,v)=mu in prints(v, " ", fundamental_weight_coordinates(mu), " ", dimension(mu)) od
Error during analysis of expression at <standard input>:14:4--16:150
Undefined identifier 'branch_irreducible'
Expression analysis failed
Command 'set special' not executed, nothing defined.
atlas> print_Z(K)
Group is semisimple
center=Z/2Z x Z/2Z x Z/2Z
atlas> set alpha=highest_root (G)
Variable alpha: vec
atlas> simple_roots (G)
Value:
| 2, -1, 0, 0 |
| -1, 2, -1, -1 |
| 0, -1, 2, 0 |
| 0, -1, 0, 2 |
atlas> simple_coroots (G)
Value:
| 1, 0, 0, 0 |
| 0, 1, 0, 0 |
| 0, 0, 1, 0 |
| 0, 0, 0, 1 |
atlas> set tau=mat:[0,0,1,0|0,1,0,0|0,0,0,1|1,0,0,0]
Variable tau: mat
atlas> tau
Value:
| 0, 0, 1, 0 |
| 0, 1, 0, 0 |
| 0, 0, 0, 1 |
| 1, 0, 0, 0 |
atlas> simple_roots (G)
Value:
| 2, -1, 0, 0 |
| -1, 2, -1, -1 |
| 0, -1, 2, 0 |
| 0, -1, 0, 2 |
atlas> tau*simple_roots (G)
Value:
| 0, -1, 2, 0 |
| -1, 2, -1, -1 |
| 0, -1, 0, 2 |
| 2, -1, 0, 0 |
atlas> delta^2
Error during analysis of expression at <standard input>:25:0-7
Undefined identifier 'delta'
Expression analysis failed
atlas>
atlas>
atlas>
atlas> tau^2
Value:
| 0, 0, 0, 1 |
| 0, 1, 0, 0 |
| 1, 0, 0, 0 |
| 0, 0, 1, 0 |
atlas> tau^3
Value:
| 1, 0, 0, 0 |
| 0, 1, 0, 0 |
| 0, 0, 1, 0 |
| 0, 0, 0, 1 |
atlas> set gamma=alpha
Variable gamma: vec
atlas> gamma
Value: [ 0, 1, 0, 0 ]
atlas> posroots (G)
Value:
| 2, -1, 0, 0, 1, -1, -1, 1, 1, -1, 1, 0 |
| -1, 2, -1, -1, 1, 1, 1, 0, 0, 0, -1, 1 |
| 0, -1, 2, 0, -1, 1, -1, 1, -1, 1, 1, 0 |
| 0, -1, 0, 2, -1, -1, 1, -1, 1, 1, 1, 0 |
atlas> gamma
Value: [ 0, 1, 0, 0 ]
atlas> set all=all_parameters_gamma (G,gamma)
Variable all: [Param]
atlas> KGB_size (G)
Value: 109
atlas> #all_parameters_gamma (G,rho(G))
Value: 196
atlas> #all
Value: 49
atlas> for p in all do prints(p) od
final parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,1,0,0]/1)
final parameter(x=108,lambda=[1,2,1,1]/1,nu=[0,1,0,0]/1)
final parameter(x=107,lambda=[3,0,3,0]/1,nu=[0,1,0,0]/1)
final parameter(x=105,lambda=[1,2,0,1]/1,nu=[0,1,0,0]/1)
final parameter(x=104,lambda=[0,1,1,1]/1,nu=[0,1,0,0]/1)
final parameter(x=103,lambda=[1,2,0,0]/1,nu=[0,1,0,0]/1)
final parameter(x=102,lambda=[1,2,0,0]/1,nu=[0,1,0,0]/1)
final parameter(x=101,lambda=[0,2,1,0]/1,nu=[0,1,0,0]/1)
final parameter(x=100,lambda=[0,2,1,0]/1,nu=[0,1,0,0]/1)
final parameter(x=99,lambda=[0,2,0,1]/1,nu=[0,1,0,0]/1)
final parameter(x=98,lambda=[0,2,0,1]/1,nu=[0,1,0,0]/1)
final parameter(x=94,lambda=[0,3,0,0]/1,nu=[0,1,0,0]/1)
final parameter(x=93,lambda=[0,3,0,0]/1,nu=[0,1,0,0]/1)
final parameter(x=92,lambda=[0,3,0,0]/1,nu=[0,1,0,0]/1)
final parameter(x=91,lambda=[0,3,0,0]/1,nu=[0,1,0,0]/1)
final parameter(x=65,lambda=[-1,4,-1,-1]/1,nu=[-1,3,-1,-1]/2)
final parameter(x=65,lambda=[-1,2,0,0]/1,nu=[-1,3,-1,-1]/2)
final parameter(x=65,lambda=[-1,5,-1,-2]/1,nu=[-1,3,-1,-1]/2)
final parameter(x=65,lambda=[-1,3,0,-1]/1,nu=[-1,3,-1,-1]/2)
final parameter(x=52,lambda=[0,2,0,-1]/1,nu=[0,1,0,-1]/1)
final parameter(x=52,lambda=[0,3,0,-2]/1,nu=[0,1,0,-1]/1)
final parameter(x=51,lambda=[0,2,0,-1]/1,nu=[0,1,0,-1]/1)
final parameter(x=51,lambda=[0,3,0,-2]/1,nu=[0,1,0,-1]/1)
final parameter(x=50,lambda=[-1,2,0,0]/1,nu=[-1,1,0,0]/1)
final parameter(x=50,lambda=[-1,2,-1,1]/1,nu=[-1,1,0,0]/1)
final parameter(x=49,lambda=[-1,2,0,0]/1,nu=[-1,1,0,0]/1)
final parameter(x=49,lambda=[-1,2,-1,1]/1,nu=[-1,1,0,0]/1)
final parameter(x=48,lambda=[0,2,-1,0]/1,nu=[0,1,-1,0]/1)
final parameter(x=48,lambda=[0,3,-2,0]/1,nu=[0,1,-1,0]/1)
final parameter(x=47,lambda=[0,2,-1,0]/1,nu=[0,1,-1,0]/1)
final parameter(x=47,lambda=[0,3,-2,0]/1,nu=[0,1,-1,0]/1)
final parameter(x=19,lambda=[0,1,0,0]/1,nu=[-1,2,-1,-1]/2)
final parameter(x=18,lambda=[0,1,0,0]/1,nu=[-1,2,-1,-1]/2)
final parameter(x=17,lambda=[0,1,0,0]/1,nu=[-1,2,-1,-1]/2)
final parameter(x=16,lambda=[0,1,0,0]/1,nu=[-1,2,-1,-1]/2)
final parameter(x=33,lambda=[1,0,1,0]/1,nu=[0,0,0,0]/1)
final parameter(x=32,lambda=[1,0,1,0]/1,nu=[0,0,0,0]/1)
final parameter(x=31,lambda=[1,0,0,1]/1,nu=[0,0,0,0]/1)
final parameter(x=30,lambda=[1,0,0,1]/1,nu=[0,0,0,0]/1)
final parameter(x=29,lambda=[0,0,1,1]/1,nu=[0,0,0,0]/1)
final parameter(x=28,lambda=[0,0,1,1]/1,nu=[0,0,0,0]/1)
final parameter(x=9,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1)
final parameter(x=7,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1)
final parameter(x=6,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1)
final parameter(x=5,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1)
final parameter(x=4,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1)
final parameter(x=3,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1)
final parameter(x=1,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1)
final parameter(x=0,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1)
Value: [(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),()]
atlas> set P=Parabolic:([0,1],KGB(G,108))
Variable P: ([int],KGBElt)
atlas> Levi(P)
Value: disconnected split real group with Lie algebra 'sl(3,R).gl(1,R).gl(1,R)'
atlas> set L=Levi(P)
Variable L: RealForm
atlas> print_Z(L)
center has 0 circle factors
center has 2 R^+ factors
finite part of center: Z/2Z x Z/2Z
atlas> components_rank (L)
Value: 2
atlas> set tl=trivial(L)
Variable tl: Param
atlas> set ind=real_induce_irreducible(tl,G)
Variable ind: ParamPol
atlas> ind
Value:
1*parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,1,0,0]/1) [0]
1*parameter(x=65,lambda=[-1,4,-1,-1]/1,nu=[-1,3,-1,-1]/2) [5]
atlas> tl
Value: final parameter(x=3,lambda=[1,1,-1,-1]/1,nu=[1,1,-1,-1]/1)
atlas> simple_roots (L)
Value:
| 2, -1 |
| -1, 2 |
| 0, -1 |
| 0, -1 |
atlas> simple_coroots (L)
Value:
| 1, 0 |
| 0, 1 |
| 0, 0 |
| 0, 0 |
atlas> highest_root (L)
Value: [ 1, 1, -1, -1 ]
atlas> rho(L)
Value: [ 1, 1, -1, -1 ]/1
atlas> monomials(ind)
Value: [final parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,1,0,0]/1),final parameter(x=65,lambda=[-1,4,-1,-1]/1,nu=[-1,3,-1,-1]/2)]
atlas> set m=$
Variable m: [Param]
atlas> set A=m[0]
Variable A: Param
atlas> set B=m[1[]
^
syntax error, unexpected ']', expecting ':'
atlas> set B=m[1]
Variable B: Param
atlas> A
Value: final parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,1,0,0]/1)
atlas> B
Value: final parameter(x=65,lambda=[-1,4,-1,-1]/1,nu=[-1,3,-1,-1]/2)
atlas> twist(tau,A)
Value: final parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,1,0,0]/1)
atlas> twist(tau,A)=A
Value: true
atlas> twist(tau,B)=B
Value: true
atlas> for i:10 do prints(all[i]) od
final parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,1,0,0]/1)
final parameter(x=108,lambda=[1,2,1,1]/1,nu=[0,1,0,0]/1)
final parameter(x=107,lambda=[3,0,3,0]/1,nu=[0,1,0,0]/1)
final parameter(x=105,lambda=[1,2,0,1]/1,nu=[0,1,0,0]/1)
final parameter(x=104,lambda=[0,1,1,1]/1,nu=[0,1,0,0]/1)
final parameter(x=103,lambda=[1,2,0,0]/1,nu=[0,1,0,0]/1)
final parameter(x=102,lambda=[1,2,0,0]/1,nu=[0,1,0,0]/1)
final parameter(x=101,lambda=[0,2,1,0]/1,nu=[0,1,0,0]/1)
final parameter(x=100,lambda=[0,2,1,0]/1,nu=[0,1,0,0]/1)
final parameter(x=99,lambda=[0,2,0,1]/1,nu=[0,1,0,0]/1)
Value: [(),(),(),(),(),(),(),(),(),()]
atlas> all[2]
Value: final parameter(x=107,lambda=[3,0,3,0]/1,nu=[0,1,0,0]/1)
atlas> twist(tau,all[2])
Value: final parameter(x=105,lambda=[1,2,0,1]/1,nu=[0,1,0,0]/1)
atlas> #all
Value: 49
atlas> set p=all[2]
Variable p: Param
atlas> p
Value: final parameter(x=107,lambda=[3,0,3,0]/1,nu=[0,1,0,0]/1)
atlas> twist(tau,p)
Value: final parameter(x=105,lambda=[1,2,0,1]/1,nu=[0,1,0,0]/1)
atlas>
atlas>
atlas>
atlas> p
Value: final parameter(x=107,lambda=[3,0,3,0]/1,nu=[0,1,0,0]/1)
atlas> twist(tau,$)
Value: final parameter(x=105,lambda=[1,2,0,1]/1,nu=[0,1,0,0]/1)
atlas> twist(tau,$)
Value: final parameter(x=104,lambda=[0,1,1,1]/1,nu=[0,1,0,0]/1)
atlas> twist(tau,$)
Value: final parameter(x=107,lambda=[3,0,3,0]/1,nu=[0,1,0,0]/1)
atlas> list(all,(int i):twist(tau,all[i])=all[i])
Error during analysis of expression at <standard input>:77:0-42
Type error:
Subexpression (all,(int i):=(twist(tau,all[i]),all[i])) at <standard input>:77:4-42
has wrong type: found ([Param],(int->bool)) while ((int->bool),int) was needed.
Expression analysis failed
atlas> list(#all,(int i):twist(tau,all[i])=all[i])
Error during analysis of expression at <standard input>:78:0-43
Type error:
Subexpression (#(all),(int i):=(twist(tau,all[i]),all[i])) at <standard input>:78:4-43
has wrong type: found (int,(int->bool)) while ((int->bool),int) was needed.
Expression analysis failed
atlas> list((int i):twist(tau,all[i])=all[i],#all)
Value: [0,1,14,15,34,41,48]
atlas> A
Value: final parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,1,0,0]/1)
atlas> LKT(A)
Value: (KGB element #108,[ 1, 1, 1, 1 ]/1)
atlas> A
Value: final parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,1,0,0]/1)
atlas> dimension(LKT(A))
Value: 1
atlas> highest_weight(LKT(A))
Value: (KGB element #0,[ 0, 0, 0, 0 ])
atlas> print_branch_irr_long (A,10)
(1+0s)*(KGB element #0,[ 0, 0, 0, 0 ]) 1 0
(1+0s)*(KGB element #0,[ 0, 1, 0, 0 ]) 16 5
(1+0s)*(KGB element #0,[ 0, 2, 0, -2 ]) 9 6
(1+0s)*(KGB element #0,[ 0, 0, 0, 2 ]) 9 6
(1+0s)*(KGB element #0,[ 0, 2, -2, 0 ]) 9 6
(1+0s)*(KGB element #0,[ 0, 0, 2, 0 ]) 9 6
(1+0s)*(KGB element #0,[ -2, 2, 0, 0 ]) 9 6
(1+0s)*(KGB element #0,[ 2, 0, 0, 0 ]) 9 6
(1+0s)*(KGB element #0,[ 1, 2, -1, -1 ]) 32 10
(1+0s)*(KGB element #0,[ -1, 2, 1, -1 ]) 32 10
(1+0s)*(KGB element #0,[ -1, 2, -1, 1 ]) 32 10
(1+0s)*(KGB element #0,[ 1, 0, 1, 1 ]) 32 10
atlas> set br=branch_irr (A,10)
Variable br: ParamPol
atlas> for mu in br do prints(mu, " ", fundamental_weight_coordinates (mu), " ", dimension(mu))
G > od
Error in expression fundamental_weight_coordinates(mu) at <standard input>:87:32-67
Failed to match 'fundamental_weight_coordinates' with argument type Split
Expression analysis failed
atlas> whattype br?
No overloads for 'br'
atlas> br
Value:
1*parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,0,0,0]/1) [0]
1*parameter(x=46,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [5]
1*parameter(x=33,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [6]
1*parameter(x=32,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [6]
1*parameter(x=31,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [6]
1*parameter(x=30,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [6]
1*parameter(x=29,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [6]
1*parameter(x=28,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [6]
1*parameter(x=7,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1) [10]
1*parameter(x=6,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1) [10]
1*parameter(x=5,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1) [10]
1*parameter(x=0,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1) [10]
atlas> for @mu in br do prints(mu, " ", fundamental_weight_coordinates (mu), " ", dimension(mu))
G > od
Runtime error:
representation is infinite dimensional
(in call at basic.at:8:57-71 of error@string, built-in)
[b=false, message="representation is infinite dimensional"]
(in call at finite_dimensional.at:12:2-75 of assert@(bool,string), defined at basic.at:8:4-74)
[p=final parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,0,0,0]/1)]
(in call at finite_dimensional.at:35:4-13 of fd_only@Param, defined at finite_dimensional.at:11:4--12:78)
[p=final parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,0,0,0]/1)]
(in call at finite_dimensional.at:42:26-62 of highest_weight_finite_dimensional@Param, defined at finite_dimensional.at:34:4--35:80)
[p=final parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,0,0,0]/1)]
(in call at <standard input>:91:33-68 of fundamental_weight_coordinates@Param, defined at finite_dimensional.at:41:4--42:77)
Evaluation aborted.
atlas> special(A,10)
Error during analysis of expression at <standard input>:93:0-13
Undefined identifier 'special'
Expression analysis failed
atlas> <savin.at
Starting to read from file 'savin.at'.
Defined print_LKTs: (Param->)
Variable G: RealForm (overriding previous instance, which had type RealForm)
Variable bourbaki_simple_roots: mat
Variable bourbaki_simple_coroots: mat
Variable C: (mat,string,int) (overriding previous instance, which had type string (constant))
Variable D: (mat,string,int)
Defined nu_bourbaki: (rat,rat->ratvec)
Added definition [5] of nu: (rat,rat->ratvec)
Defined ps: (rat,rat->Param)
Variable p: Param (overriding previous instance, which had type Param)
Variable delta: mat
Variable x: KGBElt
Variable P: ([int],KGBElt) (overriding previous instance, which had type ([int],KGBElt))
Variable L_P: RealForm
Variable t_P: Param
Variable ind_P: ParamPol
Variable parameters_ind_P: [Param]
Variable lkt_of_parameters_ind_P: [(KGBElt,ratvec)]
Variable K0_lkt_of_parameters_ind_P: [Param]
Variable highest_weights_ind_P: [(KGBElt,vec)]
Variable mu: Param
Variable K: RealForm (overriding previous instance, which had type RealForm)
Variable scr_K: mat
Variable A: Param (overriding previous instance, which had type Param)
Variable B: Param (overriding previous instance, which had type Param)
Variable Q: ([int],KGBElt)
Variable L_Q: RealForm
Variable t_Q: Param
Variable p_Q: Param
Variable ind_Q: ParamPol
Variable parameters_Q: [Param]
Variable lkt_of_parameters_Q: [(KGBElt,ratvec)]
Variable K0_lkt_of_parameters_Q: [Param]
Variable highest_weights_ind_Q: [(KGBElt,vec)]
Variable mu: Param (overriding previous instance, which had type Param)
Variable K: RealForm (overriding previous instance, which had type RealForm)
Variable scr_K: mat (overriding previous instance, which had type mat)
Added definition [2] of list: ([(KGBElt,vec)]->[void])
Defined show_K_type: (KGBElt,ratvec->)
Defined show_K_type_compact: (KGBElt,ratvec->)
Defined show_K_types: ([(KGBElt,ratvec)]->[void])
Defined show_K_types_compact: ([(KGBElt,ratvec)]->[void])
Defined branch_string: (Param,int->[void])
Variable block_A: [Param]
Variable ps_rho: [Param]
Variable ps_special: [Param]
Variable p: Param (overriding previous instance, which had type Param)
Variable all: [Param] (overriding previous instance, which had type [Param])
Defined check: (Param,int->[void])
Added definition [2] of check: (int->[(Param,int)])
Added definition [4] of test: (->)
Added definition [5] of test: (int->[void])
Variable irrps: Param
Added definition [2] of test1: (->)
Variable mu_A: (KGBElt,ratvec)
Variable mu_B: (KGBElt,ratvec)
Added definition [2] of test2: (->)
Defined test3: (->)
Defined test4: (->)
Defined test5: (->)
Defined testall: (->)
Error during analysis of expression at savin.at:180:4--182:150
Undefined identifier 'branch_irreducible' at savin.at:181:7-25
Expression analysis failed
Command 'set special' not executed, nothing defined.
Abandoning reading of file 'savin.at' at line 182
atlas> special(A,10)
Error during analysis of expression at <standard input>:96:0-13
Undefined identifier 'special'
Expression analysis failed
atlas> for @p in br do prints(LKT(p), " ", fundamental_weight_coordinates (LKT(p)), " ", dimension(LKT(p)))
G > od
Error in expression fundamental_weight_coordinates(LKT(p)) at <standard input>:97:36-75
Failed to match 'fundamental_weight_coordinates' with argument type (KGBElt,ratvec)
Expression analysis failed
atlas> br
Value:
1*parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,0,0,0]/1) [0]
1*parameter(x=46,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [5]
1*parameter(x=33,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [6]
1*parameter(x=32,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [6]
1*parameter(x=31,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [6]
1*parameter(x=30,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [6]
1*parameter(x=29,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [6]
1*parameter(x=28,lambda=[1,-1,1,1]/1,nu=[0,0,0,0]/1) [6]
1*parameter(x=7,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1) [10]
1*parameter(x=6,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1) [10]
1*parameter(x=5,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1) [10]
1*parameter(x=0,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1) [10]
atlas> set mbr=monomials (br)
Variable mbr: [Param]
atlas> set q=mbr[0]
Variable q: Param
atlas> q
Value: final parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,0,0,0]/1)
atlas> highest_weight(q)
Value: (KGB element #0,[ 0, 0, 0, 0 ])
atlas> fundamental_weight_coordinates(highest_weight(q))
Value: [ 0, 0, 0, 0 ]
atlas> for a in mbr do prints(fundamental_weight_coordinates (highest_weight(a)) od
^^
syntax error, unexpected OD, expecting ')'
atlas> for a in mbr do prints(fundamental_weight_coordinates (highest_weight(a))) od
[ 0, 0, 0, 0 ]
[ 1, 1, 1, 1 ]
[ 0, 0, 2, 2 ]
[ 0, 0, 2, 2 ]
[ 0, 2, 0, 2 ]
[ 0, 2, 0, 2 ]
[ 0, 2, 2, 0 ]
[ 2, 0, 0, 2 ]
[ 1, 1, 1, 3 ]
[ 1, 1, 1, 3 ]
[ 1, 1, 1, 3 ]
[ 1, 1, 1, 3 ]
Value: [(),(),(),(),(),(),(),(),(),(),(),()]
atlas> for a in mbr do prints(fundamental_weight_coordinates (highest_weight(a)), dimension(LKT(a)) od
^^
syntax error, unexpected OD, expecting ')'
atlas> for a in mbr do prints(fundamental_weight_coordinates (highest_weight(a)), dimension(LKT(a))) od
[ 0, 0, 0, 0 ]1
[ 1, 1, 1, 1 ]16
[ 0, 0, 2, 2 ]9
[ 0, 0, 2, 2 ]9
[ 0, 2, 0, 2 ]9
[ 0, 2, 0, 2 ]9
[ 0, 2, 2, 0 ]9
[ 2, 0, 0, 2 ]9
[ 1, 1, 1, 3 ]32
[ 1, 1, 1, 3 ]32
[ 1, 1, 1, 3 ]32
[ 1, 1, 1, 3 ]32
Value: [(),(),(),(),(),(),(),(),(),(),(),()]
atlas> print_branch_irr_long (A,10)
(1+0s)*(KGB element #0,[ 0, 0, 0, 0 ]) 1 0
(1+0s)*(KGB element #0,[ 0, 1, 0, 0 ]) 16 5
(1+0s)*(KGB element #0,[ 0, 2, 0, -2 ]) 9 6
(1+0s)*(KGB element #0,[ 0, 0, 0, 2 ]) 9 6
(1+0s)*(KGB element #0,[ 0, 2, -2, 0 ]) 9 6
(1+0s)*(KGB element #0,[ 0, 0, 2, 0 ]) 9 6
(1+0s)*(KGB element #0,[ -2, 2, 0, 0 ]) 9 6
(1+0s)*(KGB element #0,[ 2, 0, 0, 0 ]) 9 6
(1+0s)*(KGB element #0,[ 1, 2, -1, -1 ]) 32 10
(1+0s)*(KGB element #0,[ -1, 2, 1, -1 ]) 32 10
(1+0s)*(KGB element #0,[ -1, 2, -1, 1 ]) 32 10
(1+0s)*(KGB element #0,[ 1, 0, 1, 1 ]) 32 10
atlas> for a in mbr do prints(highest_weight(a), " ", fundamental_weight_coordinates (highest_weight(a)), dimension(LKT(a))) od
(KGB element #0,[ 0, 0, 0, 0 ]) [ 0, 0, 0, 0 ]1
(KGB element #0,[ 0, 1, 0, 0 ]) [ 1, 1, 1, 1 ]16
(KGB element #4,[ 0, 0, 0, 2 ]) [ 0, 0, 2, 2 ]9
(KGB element #0,[ 0, 0, 0, 2 ]) [ 0, 0, 2, 2 ]9
(KGB element #3,[ 0, 0, 2, 0 ]) [ 0, 2, 0, 2 ]9
(KGB element #0,[ 0, 0, 2, 0 ]) [ 0, 2, 0, 2 ]9
(KGB element #1,[ 2, 0, 0, 0 ]) [ 0, 2, 2, 0 ]9
(KGB element #0,[ 2, 0, 0, 0 ]) [ 2, 0, 0, 2 ]9
(KGB element #7,[ 1, 0, 1, 1 ]) [ 1, 1, 1, 3 ]32
(KGB element #6,[ 1, 0, 1, 1 ]) [ 1, 1, 1, 3 ]32
(KGB element #5,[ 1, 0, 1, 1 ]) [ 1, 1, 1, 3 ]32
(KGB element #0,[ 1, 0, 1, 1 ]) [ 1, 1, 1, 3 ]32
Value: [(),(),(),(),(),(),(),(),(),(),(),()]
atlas> for a in mbr do prints(fundamental_weight_coordinates (highest_weight(a)), dimension(LKT(a))) od
[ 0, 0, 0, 0 ]1
[ 1, 1, 1, 1 ]16
[ 0, 0, 2, 2 ]9
[ 0, 0, 2, 2 ]9
[ 0, 2, 0, 2 ]9
[ 0, 2, 0, 2 ]9
[ 0, 2, 2, 0 ]9
[ 2, 0, 0, 2 ]9
[ 1, 1, 1, 3 ]32
[ 1, 1, 1, 3 ]32
[ 1, 1, 1, 3 ]32
[ 1, 1, 1, 3 ]32
Value: [(),(),(),(),(),(),(),(),(),(),(),()]
atlas> set x=KGB(G,0)
Variable x: KGBElt (overriding previous instance, which had type KGBElt)
atlas> for a in mbr do prints(fundamental_weight_coordinates (highest_weight(a,x)), dimension(LKT(a))) od
Error in expression highest_weight(a,x) at <standard input>:113:55-74
Failed to match 'highest_weight' with argument type (Param,KGBElt)
Expression analysis failed
atlas> is_unitary(A)
Value: true
atlas> print_branch_irr_long (B,20)
(1+0s)*(KGB element #0,[ 0, 1, 0, 0 ]) 16 5
(1+0s)*(KGB element #0,[ -1, 3, -1, -1 ]) 27 10
(1+0s)*(KGB element #0,[ 1, 1, 1, -1 ]) 27 10
(1+0s)*(KGB element #0,[ 1, 1, -1, 1 ]) 27 10
(1+0s)*(KGB element #0,[ -1, 1, 1, 1 ]) 27 10
(1+0s)*(KGB element #0,[ 0, 2, 0, 0 ]) 81 15
(1+0s)*(KGB element #0,[ 0, 3, 0, -2 ]) 64 16
(1+0s)*(KGB element #0,[ 0, 1, 0, 2 ]) 64 16
(1+0s)*(KGB element #0,[ 0, 3, -2, 0 ]) 64 16
(1+0s)*(KGB element #0,[ 0, 1, 2, 0 ]) 64 16
(1+0s)*(KGB element #0,[ -2, 3, 0, 0 ]) 64 16
(1+0s)*(KGB element #0,[ 2, 1, 0, 0 ]) 64 16
(1+0s)*(KGB element #0,[ -1, 4, -1, -1 ]) 128 20
(1+0s)*(KGB element #0,[ 1, 3, -1, -1 ]) 135 20
(1+0s)*(KGB element #0,[ -1, 3, 1, -1 ]) 135 20
(1+0s)*(KGB element #0,[ -1, 3, -1, 1 ]) 135 20
(1+0s)*(KGB element #0,[ 1, 2, 1, -1 ]) 128 20
(1+0s)*(KGB element #0,[ 1, 2, -1, 1 ]) 128 20
(1+0s)*(KGB element #0,[ -1, 2, 1, 1 ]) 128 20
(1+0s)*(KGB element #0,[ 1, 1, 1, 1 ]) 135 20
atlas> is_unitary(B)
Value: true
atlas> set p=all[0]
Variable p: Param (overriding previous instance, which had type Param)
atlas> p
Value: final parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,1,0,0]/1)
atlas> set p=all[10]
Variable p: Param (overriding previous instance, which had type Param)
atlas> LKTs(p)[0]
Value: (KGB element #32,[ 1, -1, 1, 0 ]/1)
atlas> highest_weight(LKTs(p)[0])
Value: (KGB element #0,[ 0, 0, 0, 1 ])
atlas> fundamental_weight_coordinates(highest_weight(LKTs(p)[0]))
Value: [ 0, 0, 1, 1 ]
atlas> dimension(LKTs(p)[0])
Value: 4
atlas> for p in all do prints(fundamental_weight_coordinates(highest_weight(LKTs(p)[0]))) od
[ 0, 0, 0, 0 ]
[ 0, 0, 0, 2 ]
[ 0, 0, 1, 1 ]
[ 0, 1, 0, 1 ]
[ 0, 1, 1, 0 ]
[ 0, 1, 1, 0 ]
[ 1, 0, 0, 1 ]
[ 0, 1, 0, 1 ]
[ 0, 1, 0, 1 ]
[ 0, 0, 1, 1 ]
[ 0, 0, 1, 1 ]
[ 0, 0, 0, 2 ]
[ 0, 0, 0, 2 ]
[ 0, 0, 0, 2 ]
[ 0, 0, 0, 2 ]
[ 1, 1, 1, 1 ]
[ 0, 1, 1, 2 ]
[ 1, 1, 0, 2 ]
[ 1, 0, 1, 2 ]
[ 0, 0, 1, 3 ]
[ 0, 0, 2, 2 ]
[ 0, 0, 1, 3 ]
[ 0, 0, 2, 2 ]
[ 1, 0, 0, 3 ]
[ 0, 2, 2, 0 ]
[ 1, 0, 0, 3 ]
[ 2, 0, 0, 2 ]
[ 0, 1, 0, 3 ]
[ 0, 2, 0, 2 ]
[ 0, 1, 0, 3 ]
[ 0, 2, 0, 2 ]
[ 0, 0, 0, 4 ]
[ 0, 0, 0, 4 ]
[ 0, 0, 0, 4 ]
[ 0, 0, 0, 4 ]
[ 1, 1, 2, 2 ]
[ 1, 1, 2, 2 ]
[ 1, 2, 1, 2 ]
[ 1, 2, 1, 2 ]
[ 1, 2, 2, 1 ]
[ 2, 1, 1, 2 ]
[ 0, 2, 2, 2 ]
[ 1, 1, 1, 3 ]
[ 1, 1, 1, 3 ]
[ 1, 1, 1, 3 ]
[ 0, 2, 2, 2 ]
[ 0, 2, 2, 2 ]
[ 0, 2, 2, 2 ]
[ 1, 1, 1, 3 ]
Value: [(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),()]
atlas> for p@i in all do prints(fundamental_weight_coordinates(i, " ", highest_weight(LKTs(p)[0]))) od
Error in expression fundamental_weight_coordinates(i," ",highest_weight(LKTs(p)[0])) at <standard input>:125:25-91
Failed to match 'fundamental_weight_coordinates' with argument type (int,string,(KGBElt,vec))
Expression analysis failed
atlas> for p@i in all do prints(i, " ", fundamental_weight_coordinates(highest_weight(LKTs(p)[0]))) od
0 [ 0, 0, 0, 0 ]
1 [ 0, 0, 0, 2 ]
2 [ 0, 0, 1, 1 ]
3 [ 0, 1, 0, 1 ]
4 [ 0, 1, 1, 0 ]
5 [ 0, 1, 1, 0 ]
6 [ 1, 0, 0, 1 ]
7 [ 0, 1, 0, 1 ]
8 [ 0, 1, 0, 1 ]
9 [ 0, 0, 1, 1 ]
10 [ 0, 0, 1, 1 ]
11 [ 0, 0, 0, 2 ]
12 [ 0, 0, 0, 2 ]
13 [ 0, 0, 0, 2 ]
14 [ 0, 0, 0, 2 ]
15 [ 1, 1, 1, 1 ]
16 [ 0, 1, 1, 2 ]
17 [ 1, 1, 0, 2 ]
18 [ 1, 0, 1, 2 ]
19 [ 0, 0, 1, 3 ]
20 [ 0, 0, 2, 2 ]
21 [ 0, 0, 1, 3 ]
22 [ 0, 0, 2, 2 ]
23 [ 1, 0, 0, 3 ]
24 [ 0, 2, 2, 0 ]
25 [ 1, 0, 0, 3 ]
26 [ 2, 0, 0, 2 ]
27 [ 0, 1, 0, 3 ]
28 [ 0, 2, 0, 2 ]
29 [ 0, 1, 0, 3 ]
30 [ 0, 2, 0, 2 ]
31 [ 0, 0, 0, 4 ]
32 [ 0, 0, 0, 4 ]
33 [ 0, 0, 0, 4 ]
34 [ 0, 0, 0, 4 ]
35 [ 1, 1, 2, 2 ]
36 [ 1, 1, 2, 2 ]
37 [ 1, 2, 1, 2 ]
38 [ 1, 2, 1, 2 ]
39 [ 1, 2, 2, 1 ]
40 [ 2, 1, 1, 2 ]
41 [ 0, 2, 2, 2 ]
42 [ 1, 1, 1, 3 ]
43 [ 1, 1, 1, 3 ]
44 [ 1, 1, 1, 3 ]
45 [ 0, 2, 2, 2 ]
46 [ 0, 2, 2, 2 ]
47 [ 0, 2, 2, 2 ]
48 [ 1, 1, 1, 3 ]
Value: [(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),()]
atlas> set p=all[15]
Variable p: Param (overriding previous instance, which had type Param)
atlas> fundamental_weight_coordinates(highest_weight(LKTs(p)[0]))
Value: [ 1, 1, 1, 1 ]
atlas> p
Value: final parameter(x=65,lambda=[-1,4,-1,-1]/1,nu=[-1,3,-1,-1]/2)
atlas> print_branch_irr_long (p, 10)
(1+0s)*(KGB element #0,[ 0, 1, 0, 0 ]) 16 5
(1+0s)*(KGB element #0,[ -1, 3, -1, -1 ]) 27 10
(1+0s)*(KGB element #0,[ 1, 1, 1, -1 ]) 27 10
(1+0s)*(KGB element #0,[ 1, 1, -1, 1 ]) 27 10
(1+0s)*(KGB element #0,[ -1, 1, 1, 1 ]) 27 10
atlas> G:=Spin(5,3)
Value: connected quasisplit real group with Lie algebra 'so(5,3)'
atlas> all:=all_parameters_gamma (G,gamma)
Value: [final parameter(x=36,lambda=[1,2,0,0]/1,nu=[0,1,0,0]/1),final parameter(x=36,lambda=[1,2,1,-1]/1,nu=[0,1,0,0]/1),final parameter(x=32,lambda=[0,3,0,0]/1,nu=[0,1,0,0]/1),final parameter(x=16,lambda=[0,3,-1,-1]/1,nu=[-1,3,-1,-1]/2),final parameter(x=24,lambda=[-1,1,1,1]/1,nu=[-1,1,0,0]/1),final parameter(x=24,lambda=[-2,2,1,1]/1,nu=[-1,1,0,0]/1),final parameter(x=14,lambda=[-1,2,0,0]/1,nu=[-1,1,0,0]/1),final parameter(x=12,lambda=[-1,2,0,0]/1,nu=[-1,1,0,0]/1),final parameter(x=3,lambda=[0,1,0,0]/1,nu=[-1,2,-1,-1]/2),final parameter(x=1,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1),final parameter(x=0,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1)]
atlas> #all
Value: 11
atlas> for p in all do prints(p) od
final parameter(x=36,lambda=[1,2,0,0]/1,nu=[0,1,0,0]/1)
final parameter(x=36,lambda=[1,2,1,-1]/1,nu=[0,1,0,0]/1)
final parameter(x=32,lambda=[0,3,0,0]/1,nu=[0,1,0,0]/1)
final parameter(x=16,lambda=[0,3,-1,-1]/1,nu=[-1,3,-1,-1]/2)
final parameter(x=24,lambda=[-1,1,1,1]/1,nu=[-1,1,0,0]/1)
final parameter(x=24,lambda=[-2,2,1,1]/1,nu=[-1,1,0,0]/1)
final parameter(x=14,lambda=[-1,2,0,0]/1,nu=[-1,1,0,0]/1)
final parameter(x=12,lambda=[-1,2,0,0]/1,nu=[-1,1,0,0]/1)
final parameter(x=3,lambda=[0,1,0,0]/1,nu=[-1,2,-1,-1]/2)
final parameter(x=1,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1)
final parameter(x=0,lambda=[0,1,0,0]/1,nu=[0,0,0,0]/1)
Value: [(),(),(),(),(),(),(),(),(),(),()]
atlas> for p in all do let mu=LKTs(p)[0] in prints(mu, " ", dimension(mu)) od
(KGB element #0,[ 0, 0, 0, 0 ]/1) 3
(KGB element #24,[ -2, 1, 1, 1 ]/1) 1
(KGB element #0,[ 0, 0, 0, 0 ]/1) 3
(KGB element #4,[ 1, 0, 0, 0 ]/1) 5
(KGB element #24,[ -1, 1, 1, 1 ]/1) 5
(KGB element #2,[ 1, 0, 0, 0 ]/1) 10
(KGB element #2,[ 1, 0, 0, 0 ]/1) 10
(KGB element #0,[ 1, 0, 0, 0 ]/1) 15
(KGB element #3,[ 0, 1, 0, 0 ]/1) 30
(KGB element #1,[ 0, 1, 0, 0 ]/1) 7
(KGB element #0,[ 0, 1, 0, 0 ]/1) 25
Value: [(),(),(),(),(),(),(),(),(),(),()]
atlas> G:=Spin(4,4)
Value: connected split real group with Lie algebra 'so(4,4)'
atlas> L
Value: disconnected split real group with Lie algebra 'sl(3,R).gl(1,R).gl(1,R)'
atlas> tl
Value: final parameter(x=3,lambda=[1,1,-1,-1]/1,nu=[1,1,-1,-1]/1)
atlas> simple_coroots (L)
Value:
| 1, 0 |
| 0, 1 |
| 0, 0 |
| 0, 0 |
atlas> real_induce_irreducible(tl,G)
Value:
1*parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,1,0,0]/1) [0]
1*parameter(x=65,lambda=[-1,4,-1,-1]/1,nu=[-1,3,-1,-1]/2) [5]
atlas> real_induce_irreducible(parameter(x(tl),lambda(tl),nu(tl)),G)
Value:
1*parameter(x=108,lambda=[1,1,1,1]/1,nu=[0,1,0,0]/1) [0]
1*parameter(x=65,lambda=[-1,4,-1,-1]/1,nu=[-1,3,-1,-1]/2) [5]
atlas> real_induce_irreducible(parameter(x(tl),lambda(tl)+[0,0,1,0],nu(tl)),G)
Value:
1*parameter(x=101,lambda=[0,2,1,0]/1,nu=[0,1,0,0]/1) [0]
1*parameter(x=100,lambda=[0,2,1,0]/1,nu=[0,1,0,0]/1) [0]
atlas> real_induce_irreducible(parameter(x(tl),lambda(tl)+[0,0,0,1],nu(tl)),G)
Value:
1*parameter(x=99,lambda=[0,2,0,1]/1,nu=[0,1,0,0]/1) [0]
1*parameter(x=98,lambda=[0,2,0,1]/1,nu=[0,1,0,0]/1) [0]
atlas> real_induce_irreducible(parameter(x(tl),lambda(tl)+[0,0,1,1],nu(tl)),G)
Value:
1*parameter(x=103,lambda=[1,2,0,0]/1,nu=[0,1,0,0]/1) [0]
1*parameter(x=102,lambda=[1,2,0,0]/1,nu=[0,1,0,0]/1) [0]