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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> set G=SL(2,C)
Variable G: RealForm
atlas> G
Value: connected quasisplit real group with Lie algebra 'sl(2,C)'
atlas> simple_roots (G)
Value:
| 2, 0 |
| 0, 2 |
atlas> print_block(trivial(G))
Parameter defines element 1 of the following block:
0: 0 [C+,C+] 1 1 (*,*) (*,*) *(x=0,lam_rho= [0,0], nu= [0,0]/1) e
1: 1 [C-,C-] 0 0 (*,*) (*,*) *(x=1,lam_rho= [0,0], nu= [1,1]/1) 1xe
atlas> G:=Sp(4,C)
Value: connected quasisplit real group with Lie algebra 'sp(4,C)'
atlas> print_block(trivial(G))
Parameter defines element 7 of the following block:
0: 0 [C+,C+,C+,C+] 1 2 1 2 (*,*) (*,*) (*,*) (*,*) *(x=0,lam_rho= [0,0,0,0], nu= [0,0,0,0]/1) e
1: 1 [C-,C+,C-,C+] 0 4 0 3 (*,*) (*,*) (*,*) (*,*) *(x=1,lam_rho= [0,0,0,0], nu= [1,-1,1,-1]/2) 1xe
2: 1 [C+,C-,C+,C-] 3 0 4 0 (*,*) (*,*) (*,*) (*,*) *(x=2,lam_rho= [0,0,0,0], nu= [0,1,0,1]/1) 2xe
3: 2 [C-,C+,C+,C-] 2 6 5 1 (*,*) (*,*) (*,*) (*,*) *(x=3,lam_rho= [0,0,0,0], nu= [3,-1,1,3]/2) 1x2xe
4: 2 [C+,C-,C-,C+] 5 1 2 6 (*,*) (*,*) (*,*) (*,*) *(x=4,lam_rho= [0,0,0,0], nu= [1,3,3,-1]/2) 2x1xe
5: 3 [C-,C+,C-,C+] 4 7 3 7 (*,*) (*,*) (*,*) (*,*) *(x=5,lam_rho= [0,0,0,0], nu= [2,0,2,0]/1) 1x2x1xe
6: 3 [C+,C-,C+,C-] 7 3 7 4 (*,*) (*,*) (*,*) (*,*) *(x=6,lam_rho= [0,0,0,0], nu= [3,3,3,3]/2) 2x1x2xe
7: 4 [C-,C-,C-,C-] 6 5 6 5 (*,*) (*,*) (*,*) (*,*) *(x=7,lam_rho= [0,0,0,0], nu= [2,1,2,1]/1) 1x2x1x2xe
atlas> print_block(trivial(G))
Parameter defines element 7 of the following block:
0: 0 [C+,C+,C+,C+] 1 2 1 2 (*,*) (*,*) (*,*) (*,*) *(x=0,lam_rho= [0,0,0,0], nu= [0,0,0,0]/1) e
1: 1 [C-,C+,C-,C+] 0 4 0 3 (*,*) (*,*) (*,*) (*,*) *(x=1,lam_rho= [0,0,0,0], nu= [1,-1,1,-1]/2) 1xe
2: 1 [C+,C-,C+,C-] 3 0 4 0 (*,*) (*,*) (*,*) (*,*) *(x=2,lam_rho= [0,0,0,0], nu= [0,1,0,1]/1) 2xe
3: 2 [C-,C+,C+,C-] 2 6 5 1 (*,*) (*,*) (*,*) (*,*) *(x=3,lam_rho= [0,0,0,0], nu= [3,-1,1,3]/2) 1x2xe
4: 2 [C+,C-,C-,C+] 5 1 2 6 (*,*) (*,*) (*,*) (*,*) *(x=4,lam_rho= [0,0,0,0], nu= [1,3,3,-1]/2) 2x1xe
5: 3 [C-,C+,C-,C+] 4 7 3 7 (*,*) (*,*) (*,*) (*,*) *(x=5,lam_rho= [0,0,0,0], nu= [2,0,2,0]/1) 1x2x1xe
6: 3 [C+,C-,C+,C-] 7 3 7 4 (*,*) (*,*) (*,*) (*,*) *(x=6,lam_rho= [0,0,0,0], nu= [3,3,3,3]/2) 2x1x2xe
7: 4 [C-,C-,C-,C-] 6 5 6 5 (*,*) (*,*) (*,*) (*,*) *(x=7,lam_rho= [0,0,0,0], nu= [2,1,2,1]/1) 1x2x1x2xe
atlas> print_block(trivial(G))
Parameter defines element 7 of the following block:
0: 0 [C+,C+,C+,C+] 1 2 1 2 (*,*) (*,*) (*,*) (*,*) *(x=0,lam_rho= [0,0,0,0], nu= [0,0,0,0]/1) e
1: 1 [C-,C+,C-,C+] 0 4 0 3 (*,*) (*,*) (*,*) (*,*) *(x=1,lam_rho= [0,0,0,0], nu= [1,-1,1,-1]/2) 1xe
2: 1 [C+,C-,C+,C-] 3 0 4 0 (*,*) (*,*) (*,*) (*,*) *(x=2,lam_rho= [0,0,0,0], nu= [0,1,0,1]/1) 2xe
3: 2 [C-,C+,C+,C-] 2 6 5 1 (*,*) (*,*) (*,*) (*,*) *(x=3,lam_rho= [0,0,0,0], nu= [3,-1,1,3]/2) 1x2xe
4: 2 [C+,C-,C-,C+] 5 1 2 6 (*,*) (*,*) (*,*) (*,*) *(x=4,lam_rho= [0,0,0,0], nu= [1,3,3,-1]/2) 2x1xe
5: 3 [C-,C+,C-,C+] 4 7 3 7 (*,*) (*,*) (*,*) (*,*) *(x=5,lam_rho= [0,0,0,0], nu= [2,0,2,0]/1) 1x2x1xe
6: 3 [C+,C-,C+,C-] 7 3 7 4 (*,*) (*,*) (*,*) (*,*) *(x=6,lam_rho= [0,0,0,0], nu= [3,3,3,3]/2) 2x1x2xe
7: 4 [C-,C-,C-,C-] 6 5 6 5 (*,*) (*,*) (*,*) (*,*) *(x=7,lam_rho= [0,0,0,0], nu= [2,1,2,1]/1) 1x2x1x2xe
atlas>
atlas>
atlas>
atlas>
atlas>
atlas>
atlas> <<complex_aux.at
Starting to read from file 'complex_aux.at'.
Defined w: (Param->[int])
Defined print_complex_block: (Param->)
Defined print_complex_composition_series: (Param->)
Completely read file 'complex_aux.at'.
atlas> set G=SL(3,C)
Variable G: RealForm (overriding previous instance, which had type RealForm)
atlas> print_complex_block (trivial(G))
each line lists:', new_line, x,lambda,nu,gamma_L,gamma_R,mu_C,nu_C
0 | [ 2, 1, 2, 1 ]/1 | [ 0, 0, 0, 0 ]/1 | [ 2, 1 ]/1 | [ 2, 1 ]/1 | [ 4, 2 ] | [ 0, 0 ]/1 | []
1 | [ 2, 1, 2, 1 ]/1 | [ 1, 2, 1, 2 ]/2 | [ 2, 1 ]/1 | [ 1, -1 ]/1 | [ 3, 0 ] | [ 1, 2 ]/1 | [1]
2 | [ 2, 1, 2, 1 ]/1 | [ 1, -1, 1, -1 ]/2 | [ 2, 1 ]/1 | [ 1, 2 ]/1 | [ 3, 3 ] | [ 1, -1 ]/1 | [0]
3 | [ 2, 1, 2, 1 ]/1 | [ 3, 3, 3, 0 ]/2 | [ 2, 1 ]/1 | [ -1, -2 ]/1 | [ 1, -1 ] | [ 3, 3 ]/1 | [1,0]
4 | [ 2, 1, 2, 1 ]/1 | [ 3, 0, 3, 3 ]/2 | [ 2, 1 ]/1 | [ -1, 1 ]/1 | [ 1, 2 ] | [ 3, 0 ]/1 | [0,1]
5 | [ 2, 1, 2, 1 ]/1 | [ 2, 1, 2, 1 ]/1 | [ 2, 1 ]/1 | [ -2, -1 ]/1 | [ 0, 0 ] | [ 4, 2 ]/1 | [1,0,1]
atlas> rho(G)
Value: [ 2, 1, 2, 1 ]/1
atlas> for w in generate_W(G) do let (,v) =w in prints(v) od
[]
[0]
[1]
[2]
[3]
[1,0]
[2,0]
[3,0]
[0,1]
[2,1]
[3,1]
[3,2]
[2,3]
[0,1,0]
[2,1,0]
[3,1,0]
[3,2,0]
[2,3,0]
[2,0,1]
[3,0,1]
[3,2,1]
[2,3,1]
[2,3,2]
[2,0,1,0]
[3,0,1,0]
[3,2,1,0]
[2,3,1,0]
[2,3,2,0]
[3,2,0,1]
[2,3,0,1]
[2,3,2,1]
[3,2,0,1,0]
[2,3,0,1,0]
[2,3,2,1,0]
[2,3,2,0,1]
[2,3,2,0,1,0]
Value: [(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),()]
atlas> print_KGB(G)
kgbsize: 6
Base grading: [1111].
0: 0 [C,C,C,C] 2 1 2 1 * * * * (0,0,0,0)#0 e
1: 1 [C,C,C,C] 4 0 3 0 * * * * (0,0,0,0) 0 2xe
2: 1 [C,C,C,C] 0 3 0 4 * * * * (0,0,0,0) 0 1xe
3: 2 [C,C,C,C] 5 2 1 5 * * * * (0,0,0,0) 0 2x1xe
4: 2 [C,C,C,C] 1 5 5 2 * * * * (0,0,0,0) 0 1x2xe
5: 3 [C,C,C,C] 3 4 4 3 * * * * (0,0,0,0) 0 1x2x1xe
atlas> G:=GL(3,C)
Value: connected quasisplit real group with Lie algebra 'sl(3,C).gl(1,C)'
atlas> print_complex_
print_complex_block print_complex_composition_series
atlas> print_complex_block (trivial(G))
each line lists:', new_line, x,lambda,nu,gamma_L,gamma_R,mu_C,nu_C
0 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 0, 0, 0, 0, 0, 0 ]/1 | [ 1, 0, -1 ]/1 | [ 1, 0, -1 ]/1 | [ 2, 0, -2 ] | [ 0, 0, 0 ]/1 | []
1 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 0, 1, -1, 0, 1, -1 ]/2 | [ 1, 0, -1 ]/1 | [ 1, -1, 0 ]/1 | [ 2, -1, -1 ] | [ 0, 1, -1 ]/1 | [1]
2 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 1, -1, 0, 1, -1, 0 ]/2 | [ 1, 0, -1 ]/1 | [ 0, 1, -1 ]/1 | [ 1, 1, -2 ] | [ 1, -1, 0 ]/1 | [0]
3 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 1, 1, -2, 2, -1, -1 ]/2 | [ 1, 0, -1 ]/1 | [ 0, -1, 1 ]/1 | [ 1, -1, 0 ] | [ 1, 1, -2 ]/1 | [1,0]
4 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 2, -1, -1, 1, 1, -2 ]/2 | [ 1, 0, -1 ]/1 | [ -1, 1, 0 ]/1 | [ 0, 1, -1 ] | [ 2, -1, -1 ]/1 | [0,1]
5 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 1, 0, -1 ]/1 | [ -1, 0, 1 ]/1 | [ 0, 0, 0 ] | [ 2, 0, -2 ]/1 | [1,0,1]
atlas> print_complex_block (trivial(G))
each line lists:', new_line, x,lambda,nu,gamma_L,gamma_R,mu_C,nu_C
0 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 0, 0, 0, 0, 0, 0 ]/1 | [ 1, 0, -1 ]/1 | [ 1, 0, -1 ]/1 | [ 2, 0, -2 ] | [ 0, 0, 0 ]/1 | []
1 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 0, 1, -1, 0, 1, -1 ]/2 | [ 1, 0, -1 ]/1 | [ 1, -1, 0 ]/1 | [ 2, -1, -1 ] | [ 0, 1, -1 ]/1 | [1]
2 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 1, -1, 0, 1, -1, 0 ]/2 | [ 1, 0, -1 ]/1 | [ 0, 1, -1 ]/1 | [ 1, 1, -2 ] | [ 1, -1, 0 ]/1 | [0]
3 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 1, 1, -2, 2, -1, -1 ]/2 | [ 1, 0, -1 ]/1 | [ 0, -1, 1 ]/1 | [ 1, -1, 0 ] | [ 1, 1, -2 ]/1 | [1,0]
4 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 2, -1, -1, 1, 1, -2 ]/2 | [ 1, 0, -1 ]/1 | [ -1, 1, 0 ]/1 | [ 0, 1, -1 ] | [ 2, -1, -1 ]/1 | [0,1]
5 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 1, 0, -1, 1, 0, -1 ]/1 | [ 1, 0, -1 ]/1 | [ -1, 0, 1 ]/1 | [ 0, 0, 0 ] | [ 2, 0, -2 ]/1 | [1,0,1]
atlas>
atlas>
atlas>
atlas>
atlas> G:=SL(3,C)
Value: connected quasisplit real group with Lie algebra 'sl(3,C)'
atlas> KL_
KL_P_polynomials KL_Q_polynomial
KL_P_polynomials_alt KL_Q_polynomials
KL_P_polynomials_at_minus_one KL_block
KL_P_polynomials_old KL_block_alt
KL_P_signed_polynomials KL_inverse_mat_at_1
KL_P_signed_polynomials_at_minus_one KL_sum_at_s
KL_P_signed_polynomials_old
atlas> set p=trivial(G)
Variable p: Param
atlas> set P=KL_P_signed_polynomials(p)
Variable P: [[vec]]
atlas> P
Value: [[[ 1 ],[ -1 ],[ -1 ],[ 1 ],[ 1 ],[ -1 ]],[[ ],[ 1 ],[ ],[ -1 ],[ -1 ],[ 1 ]],[[ ],[ ],[ 1 ],[ -1 ],[ -1 ],[ 1 ]],[[ ],[ ],[ ],[ 1 ],[ ],[ -1 ]],[[ ],[ ],[ ],[ ],[ 1 ],[ -1 ]],[[ ],[ ],[ ],[ ],[ ],[ 1 ]]]
atlas> printPolyMatrix (P)
+1 -1 -1 +1 +1 -1
0 +1 0 -1 -1 +1
0 0 +1 -1 -1 +1
0 0 0 +1 0 -1
0 0 0 0 +1 -1
0 0 0 0 0 +1
atlas> set Q=KL_Q_polynomials (p)
Variable Q: [[vec]]
atlas> printPolyMatrix (Q)
+1 +1 +1 +1 +1 +1
0 +1 0 +1 +1 +1
0 0 +1 +1 +1 +1
0 0 0 +1 0 +1
0 0 0 0 +1 +1
0 0 0 0 0 +1
atlas> printPolyMatrix (P*Q)
+1 0 0 0 0 0
0 +1 0 0 0 0
0 0 +1 0 0 0
0 0 0 +1 0 0
0 0 0 0 +1 0
0 0 0 0 0 +1
atlas> print_block(p)
Parameter defines element 5 of the following block:
0: 0 [C+,C+,C+,C+] 2 1 2 1 (*,*) (*,*) (*,*) (*,*) *(x=0,lam_rho= [0,0,0,0], nu= [0,0,0,0]/1) e
1: 1 [C+,C-,C+,C-] 4 0 3 0 (*,*) (*,*) (*,*) (*,*) *(x=1,lam_rho= [0,0,0,0], nu= [1,2,1,2]/2) 2xe
2: 1 [C-,C+,C-,C+] 0 3 0 4 (*,*) (*,*) (*,*) (*,*) *(x=2,lam_rho= [0,0,0,0], nu= [1,-1,1,-1]/2) 1xe
3: 2 [C+,C-,C-,C+] 5 2 1 5 (*,*) (*,*) (*,*) (*,*) *(x=3,lam_rho= [0,0,0,0], nu= [3,3,3,0]/2) 2x1xe
4: 2 [C-,C+,C+,C-] 1 5 5 2 (*,*) (*,*) (*,*) (*,*) *(x=4,lam_rho= [0,0,0,0], nu= [3,0,3,3]/2) 1x2xe
5: 3 [C-,C-,C-,C-] 3 4 4 3 (*,*) (*,*) (*,*) (*,*) *(x=5,lam_rho= [0,0,0,0], nu= [2,1,2,1]/1) 1x2x1xe
atlas> print_complex_block (p)
each line lists:', new_line, x,lambda,nu,gamma_L,gamma_R,mu_C,nu_C
0 | [ 2, 1, 2, 1 ]/1 | [ 0, 0, 0, 0 ]/1 | [ 2, 1 ]/1 | [ 2, 1 ]/1 | [ 4, 2 ] | [ 0, 0 ]/1 | []
1 | [ 2, 1, 2, 1 ]/1 | [ 1, 2, 1, 2 ]/2 | [ 2, 1 ]/1 | [ 1, -1 ]/1 | [ 3, 0 ] | [ 1, 2 ]/1 | [1]
2 | [ 2, 1, 2, 1 ]/1 | [ 1, -1, 1, -1 ]/2 | [ 2, 1 ]/1 | [ 1, 2 ]/1 | [ 3, 3 ] | [ 1, -1 ]/1 | [0]
3 | [ 2, 1, 2, 1 ]/1 | [ 3, 3, 3, 0 ]/2 | [ 2, 1 ]/1 | [ -1, -2 ]/1 | [ 1, -1 ] | [ 3, 3 ]/1 | [1,0]
4 | [ 2, 1, 2, 1 ]/1 | [ 3, 0, 3, 3 ]/2 | [ 2, 1 ]/1 | [ -1, 1 ]/1 | [ 1, 2 ] | [ 3, 0 ]/1 | [0,1]
5 | [ 2, 1, 2, 1 ]/1 | [ 2, 1, 2, 1 ]/1 | [ 2, 1 ]/1 | [ -2, -1 ]/1 | [ 0, 0 ] | [ 4, 2 ]/1 | [1,0,1]
atlas> print_character_formula (p)
1*final parameter(x=5,lambda=[2,1,2,1]/1,nu=[2,1,2,1]/1)
-1*final parameter(x=4,lambda=[2,1,2,1]/1,nu=[3,0,3,3]/2)
-1*final parameter(x=3,lambda=[2,1,2,1]/1,nu=[3,3,3,0]/2)
1*final parameter(x=2,lambda=[2,1,2,1]/1,nu=[1,-1,1,-1]/2)
1*final parameter(x=1,lambda=[2,1,2,1]/1,nu=[1,2,1,2]/2)
-1*final parameter(x=0,lambda=[2,1,2,1]/1,nu=[0,0,0,0]/1)
atlas> print_composition_series (p)
1*final parameter(x=5,lambda=[2,1,2,1]/1,nu=[2,1,2,1]/1)
1*final parameter(x=4,lambda=[2,1,2,1]/1,nu=[3,0,3,3]/2)
1*final parameter(x=3,lambda=[2,1,2,1]/1,nu=[3,3,3,0]/2)
1*final parameter(x=2,lambda=[2,1,2,1]/1,nu=[1,-1,1,-1]/2)
1*final parameter(x=1,lambda=[2,1,2,1]/1,nu=[1,2,1,2]/2)
1*final parameter(x=0,lambda=[2,1,2,1]/1,nu=[0,0,0,0]/1)
atlas> print_composition_series (B[4])
Error during analysis of expression at <standard input>:40:0-31
Undefined identifier 'B'
Expression analysis failed
atlas> set B=block_of (p)
Variable B: [Param]
atlas> print_composition_series (B[4])
1*final parameter(x=4,lambda=[2,1,2,1]/1,nu=[3,0,3,3]/2)
1*final parameter(x=2,lambda=[2,1,2,1]/1,nu=[1,-1,1,-1]/2)
1*final parameter(x=1,lambda=[2,1,2,1]/1,nu=[1,2,1,2]/2)
1*final parameter(x=0,lambda=[2,1,2,1]/1,nu=[0,0,0,0]/1)
atlas> printPolyMatrix (Q)
+1 +1 +1 +1 +1 +1
0 +1 0 +1 +1 +1
0 0 +1 +1 +1 +1
0 0 0 +1 0 +1
0 0 0 0 +1 +1
0 0 0 0 0 +1
atlas> set G=SL(3,C)
Variable G: RealForm (overriding previous instance, which had type RealForm)
atlas> set p=trivial(G)
Variable p: Param (overriding previous instance, which had type Param)
atlas> set P=KL_P_signed_polynomials(p)
Variable P: [[vec]] (overriding previous instance, which had type [[vec]])
atlas> printPolyMatrix (P)
+1 -1 -1 +1 +1 -1
0 +1 0 -1 -1 +1
0 0 +1 -1 -1 +1
0 0 0 +1 0 -1
0 0 0 0 +1 -1
0 0 0 0 0 +1
atlas> p
Value: final parameter(x=5,lambda=[2,1,2,1]/1,nu=[2,1,2,1]/1)
atlas> G:=SL(4,C)
Value: connected quasisplit real group with Lie algebra 'sl(4,C)'
atlas> set p=trivial(G)
Variable p: Param (overriding previous instance, which had type Param)
atlas> set P=KL_P_signed_polynomials(p)
Variable P: [[vec]] (overriding previous instance, which had type [[vec]])
atlas> printPolyMatrix (P)
+1 -1 -1 -1 +1 +1 +1 +1 +1 -1 -1 -1 -1 -1 -1 +1 +1+q +1 +1 +1 -1 -1-q -1 +1
0 +1 0 0 -1 -1 0 -1 0 +1 +1 +1 +1 +1 0 -1 -1 -1 -1 -1 +1 +1+q +1 -1
0 0 +1 0 -1 -1 -1 0 -1 +1 +1 +1 +1 +1 +1 -1 -1-q -1 -1 -1 +1 +1 +1 -1
0 0 0 +1 0 0 -1 -1 -1 +1 0 +1 +1 +1 +1 -1 -1 -1 -1 -1 +1 +1+q +1 -1
0 0 0 0 +1 0 0 0 0 -1 -1 0 -1 0 0 +1 +1 +1 +1 0 -1 -1 -1 +1
0 0 0 0 0 +1 0 0 0 0 -1 -1 0 -1 0 +1 +1 0 +1 +1 -1 -1 -1 +1
0 0 0 0 0 0 +1 0 0 -1 0 -1 0 0 -1 +1 +1 +1 0 +1 -1 -1 -1 +1
0 0 0 0 0 0 0 +1 0 -1 0 -1 -1 -1 0 +1 +1 +1 +1 +1 -1 -1-q -1 +1
0 0 0 0 0 0 0 0 +1 0 0 0 -1 -1 -1 0 +1 +1 +1 +1 -1 -1 -1 +1
0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 -1 0 -1 0 0 +1 +1 0 -1
0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 -1 -1 0 -1 0 +1 +1 +1 -1
0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 -1 -1 0 0 -1 +1 +1 +1 -1
0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 -1 -1 -1 0 +1 +1 +1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 -1 -1 0 +1 +1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 -1 -1 0 -1 +1 +1 +1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 -1 -1 0 +1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 -1 0 -1 +1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 -1 -1 0 +1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 -1 -1 +1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 -1 -1 +1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1
atlas> printPolyMatrix (P)
+1 -1 -1 -1 +1 +1 +1 +1 +1 -1 -1 -1 -1 -1 -1 +1 +1+q +1 +1 +1 -1 -1-q -1 +1
0 +1 0 0 -1 -1 0 -1 0 +1 +1 +1 +1 +1 0 -1 -1 -1 -1 -1 +1 +1+q +1 -1
0 0 +1 0 -1 -1 -1 0 -1 +1 +1 +1 +1 +1 +1 -1 -1-q -1 -1 -1 +1 +1 +1 -1
0 0 0 +1 0 0 -1 -1 -1 +1 0 +1 +1 +1 +1 -1 -1 -1 -1 -1 +1 +1+q +1 -1
0 0 0 0 +1 0 0 0 0 -1 -1 0 -1 0 0 +1 +1 +1 +1 0 -1 -1 -1 +1
0 0 0 0 0 +1 0 0 0 0 -1 -1 0 -1 0 +1 +1 0 +1 +1 -1 -1 -1 +1
0 0 0 0 0 0 +1 0 0 -1 0 -1 0 0 -1 +1 +1 +1 0 +1 -1 -1 -1 +1
0 0 0 0 0 0 0 +1 0 -1 0 -1 -1 -1 0 +1 +1 +1 +1 +1 -1 -1-q -1 +1
0 0 0 0 0 0 0 0 +1 0 0 0 -1 -1 -1 0 +1 +1 +1 +1 -1 -1 -1 +1
0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 -1 0 -1 0 0 +1 +1 0 -1
0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 -1 -1 0 -1 0 +1 +1 +1 -1
0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 -1 -1 0 0 -1 +1 +1 +1 -1
0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 -1 -1 -1 0 +1 +1 +1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 -1 -1 0 +1 +1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 -1 -1 0 -1 +1 +1 +1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 -1 -1 0 +1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 -1 0 -1 +1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 -1 -1 0 +1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 -1 -1 +1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 -1 -1 +1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1
atlas>
atlas>
atlas>
atlas>
atlas>
atlas> jantezen(p)
Error during analysis of expression at <standard input>:59:0-11
Undefined identifier 'jantezen'
Expression analysis failed
atlas> <jantzen.at
atlas> whattype jantzen?
No overloads for 'jantzen'
atlas>
atlas>
atlas>
atlas>
atlas>
atlas>
atlas>
atlas>
atlas>
atlas>
atlas> <<jantzen.at
Starting to read from file 'jantzen.at'.
Redefined graded_multiplicities: ([Param],[[vec]],Param,Param->vec)
Redefined graded_multiplicities: ([Param],Param,Param->vec)
Redefined graded_multiplicities: (Param,Param->vec)
Redefined graded_composition_series: ([Param],[[vec]],Param->[(Param,vec)])
Redefined graded_composition_series: ([Param],Param->[(Param,vec)])
Redefined graded_composition_series: (Param->[(Param,vec)])
Redefined print_graded_composition_series: (Param->)
Completely read file 'jantzen.at'.
atlas> graded_multiplicities (p)
Error in expression graded_multiplicities(p) at <standard input>:73:0-25
Failed to match 'graded_multiplicities' with argument type Param
Expression analysis failed
atlas> print_graded_composition_series (p)
G=connected quasisplit real group with Lie algebra 'sl(4,C)'
graded composition series of standard module:
final parameter(x=23,lambda=[3,2,1,3,2,1]/1,nu=[3,2,1,3,2,1]/1)
length=6
l=length, ld=length difference, Q=Q(irr,std)
parameter l ld Q
final parameter(x=0,lambda=[3,2,1,3,2,1]/1,nu=[0,0,0,0,0,0]/1) 0 6 +1 [0 . 0 . 0 . 1 ]
final parameter(x=1,lambda=[3,2,1,3,2,1]/1,nu=[1,1,2,1,1,2]/2) 1 5 +1 [. 0 . 0 . 1 . ]
final parameter(x=2,lambda=[3,2,1,3,2,1]/1,nu=[0,1,-1,0,1,-1]/2) 1 5 +1+q [. 0 . 1 . 1 . ]
final parameter(x=3,lambda=[3,2,1,3,2,1]/1,nu=[1,-1,0,1,-1,0]/2) 1 5 +1 [. 0 . 0 . 1 . ]
final parameter(x=4,lambda=[3,2,1,3,2,1]/1,nu=[2,3,3,1,3,0]/2) 2 4 +1 [0 . 0 . 1 . . ]
final parameter(x=5,lambda=[3,2,1,3,2,1]/1,nu=[1,3,0,2,3,3]/2) 2 4 +1 [0 . 0 . 1 . . ]
final parameter(x=6,lambda=[3,2,1,3,2,1]/1,nu=[1,1,-2,2,-1,-1]/2) 2 4 +1 [0 . 0 . 1 . . ]
final parameter(x=7,lambda=[3,2,1,3,2,1]/1,nu=[1,0,1,1,0,1]/1) 2 4 +1+q [0 . 1 . 1 . . ]
final parameter(x=8,lambda=[3,2,1,3,2,1]/1,nu=[2,-1,-1,1,1,-2]/2) 2 4 +1 [0 . 0 . 1 . . ]
final parameter(x=9,lambda=[3,2,1,3,2,1]/1,nu=[2,2,2,2,0,0]/1) 3 3 +1 [. 0 . 1 . . . ]
final parameter(x=10,lambda=[3,2,1,3,2,1]/1,nu=[1,2,1,1,2,1]/1) 3 3 +1 [. 0 . 1 . . . ]
final parameter(x=11,lambda=[3,2,1,3,2,1]/1,nu=[2,3,-1,4,1,3]/2) 3 3 +1 [. 0 . 1 . . . ]
final parameter(x=12,lambda=[3,2,1,3,2,1]/1,nu=[4,1,3,2,3,-1]/2) 3 3 +1 [. 0 . 1 . . . ]
final parameter(x=13,lambda=[3,2,1,3,2,1]/1,nu=[2,0,0,2,2,2]/1) 3 3 +1 [. 0 . 1 . . . ]
final parameter(x=14,lambda=[3,2,1,3,2,1]/1,nu=[1,0,-1,1,0,-1]/1) 3 3 +1 [. 0 . 1 . . . ]
final parameter(x=15,lambda=[3,2,1,3,2,1]/1,nu=[4,5,3,5,1,2]/2) 4 2 +1 [0 . 1 . . . . ]
final parameter(x=16,lambda=[3,2,1,3,2,1]/1,nu=[2,2,0,2,2,0]/1) 4 2 +1 [0 . 1 . . . . ]
final parameter(x=17,lambda=[3,2,1,3,2,1]/1,nu=[5,3,4,4,1,-1]/2) 4 2 +1 [0 . 1 . . . . ]
final parameter(x=18,lambda=[3,2,1,3,2,1]/1,nu=[5,1,2,4,5,3]/2) 4 2 +1 [0 . 1 . . . . ]
final parameter(x=19,lambda=[3,2,1,3,2,1]/1,nu=[4,1,-1,5,3,4]/2) 4 2 +1 [0 . 1 . . . . ]
final parameter(x=20,lambda=[3,2,1,3,2,1]/1,nu=[5,5,2,5,3,0]/2) 5 1 +1 [. 1 . . . . . ]
final parameter(x=21,lambda=[3,2,1,3,2,1]/1,nu=[6,3,3,6,3,3]/2) 5 1 +1 [. 1 . . . . . ]
final parameter(x=22,lambda=[3,2,1,3,2,1]/1,nu=[5,3,0,5,5,2]/2) 5 1 +1 [. 1 . . . . . ]
final parameter(x=23,lambda=[3,2,1,3,2,1]/1,nu=[3,2,1,3,2,1]/1) 6 0 +1 [1 . . . . . . ]
atlas>