Atlas of Lie Groups and Representations

Documentation contents

Script File

sommers.at

Source
atlas-scripts/sommers.at (557 lines)
Definitions
76
Loads
Loaded by
none of the other all.at files

Definitions in source order

partition_sum

L6partition_sum(Partition P,Partition Q) = Partition

multiplicity

L9multiplicity = multiplicity(=@(int,int))

also defined in basic.at

add_one

L11add_one(Partition P) = Partition

subtract_one

L12subtract_one(Partition P) = Partition

dual_orbit

L14dual_orbit(Partition P)

also in this file at line 236, line 258

complex_nilpotent_from_partition

L22complex_nilpotent_from_partition(RootDatum rd, Partition p) = ComplexNilpotent

dim_nilpotent_partition

L25dim_nilpotent_partition(RootDatum rd,Partition p)

star

L28star (bool b) = string
return a star if the condition is met, else empty

print_nilpotent_orbit_partitions

L66print_nilpotent_orbit_partitions(RootDatum rd,[vec] orbits)

also in this file at line 31

ClassicalOrbitSymbol type

L78
set_type ClassicalOrbitSymbol=(int,([int,int,bool]),int)

OrbitSymbol type

L79
set_type OrbitSymbol=([(int,int)],ClassicalOrbitSymbol)

first

L81first(ClassicalOrbitSymbol (a,,))

also in this file at line 145; also defined in basic.at

last

L82last(ClassicalOrbitSymbol (,,a))

also in this file at line 146; also defined in basic.at

middle

L83middle(ClassicalOrbitSymbol (,a,))

also in this file at line 147

GL_part

L85GL_part(OrbitSymbol (pairs,)) = [(int,int)]

also in this file at line 266

classical_part

L86classical_part(OrbitSymbol (,qdsymbol)) = ClassicalOrbitSymbol

sum 2 overloads

L88sum(ClassicalOrbitSymbol S)
L91sum(OrbitSymbol S)

also defined in basic.at

root_datum

L94root_datum(OrbitSymbol S)

also in this file at line 195; also defined in basic.at, W_reps.at, K_Nilpotent.at

partitions_all_even_parts

L98partitions_all_even_parts(int n)

partitions_all_odd_parts

L102partitions_all_odd_parts(int n)

cores

L107cores(int n)

underlying_orbit

L132underlying_orbit(OrbitSymbol S)

first

L145first(ClassicalOrbitSymbol (b,,)) = int

also in this file at line 81; also defined in basic.at

last

L146last(ClassicalOrbitSymbol (,,a)) = int

also in this file at line 82; also defined in basic.at

middle

L147middle(ClassicalOrbitSymbol (,middle,)) = [(int,int,bool)]

also in this file at line 83

validate_signs

L149validate_signs(int first,[(int,int,bool)] m,int last) = bool

rank

L161rank(ClassicalOrbitSymbol (first,middle,last)) = int

also defined in basic.at, combinatorics.at

core

L164core(ClassicalOrbitSymbol (a,b,c))

validate 2 overloads

L167validate(ClassicalOrbitSymbol (first,middle,last)) = bool
L175validate(OrbitSymbol S) = bool

root_datum

L195root_datum(ClassicalOrbitSymbol S)

also in this file at line 94; also defined in basic.at, W_reps.at, K_Nilpotent.at

signs

L199signs((int,[(int,int,bool)],int) S)

valid_signs

L210valid_signs((int,[(int,int)],int) S)

dual_data

L221dual_data(int n)

dual_symbols

L224dual_symbols(int n)

q

L227q(ClassicalOrbitSymbol S) = Partition

also defined in L_packet.at

p

L233p(ClassicalOrbitSymbol S)

dual_orbit 2 overloads

L236dual_orbit(ClassicalOrbitSymbol S)
L258dual_orbit(OrbitSymbol S) = Partition

also in this file at line 14

GL_part

L266GL_part(Partition P)

also in this file at line 85

parts_C

L270parts_C(Partition P)

parts_B

L294parts_B(Partition P)

classical_part_C

L319classical_part_C(Partition P)

classical_part_B

L323classical_part_B(Partition P)

default_orbit_symbol_C

L327default_orbit_symbol_C(Partition P)

default_orbit_symbol_B

L332default_orbit_symbol_B(Partition P)

default_orbit_symbol

L338default_orbit_symbol(Partition P)

ungroup

L341ungroup(ClassicalOrbitSymbol S)

regroup

L346regroup(Partition P)

delete_all 2 overloads

L354delete_all(int i,[int] list)
L357delete_all([int] deletes,[int] list)

variants_C

L361variants_C(ClassicalOrbitSymbol S)

also in this file at line 405

variants_B

L381variants_B(ClassicalOrbitSymbol S)

also in this file at line 410

sort

L402sort([(int,int)] list)

variants_C

L405variants_C(OrbitSymbol S)

also in this file at line 361

variants_B

L410variants_B(OrbitSymbol S)

also in this file at line 381

orbit_symbols_C

L415orbit_symbols_C(Partition P)

orbit_symbols_B

L420orbit_symbols_B(Partition P)

orbit_symbols

L425orbit_symbols(Partition P)

also in this file at line 441

sort_by_dual_orbit

L428sort_by_dual_orbit = ([OrbitSymbol]->[OrbitSymbol])

birational_induction 2 overloads

L431birational_induction(OrbitSymbol S)
L437birational_induction(OrbitSymbol S)

orbit_symbols

L441orbit_symbols(RootDatum rd) = [OrbitSymbol]

also in this file at line 425

valid_symbols

L445valid_symbols(RootDatum rd) = [OrbitSymbol]

chain

L450chain(int a, int b)

infinitesimal_character_old

L454infinitesimal_character_old(OrbitSymbol S)
let v=##(##([a,b,c,d])) then
(num,denom)=%v in
ratvec:reverse_sort(for a in num do abs(a) od)/denom
L468

infinitesimal_character

L473infinitesimal_character(OrbitSymbol S)

also defined in basic.at, modules.at

is_distinguished

L489is_distinguished(OrbitSymbol S) = bool
and all(for (,,x) in cl.middle do not x od)
L491

is_birigid

L493is_birigid(Partition P) = bool

test

L495test(RootDatum rd)

also in this file at line 539; also defined in test_unitarity.at, all_finite_order.at, nilpotent_centralizer.at

test_valid_only

L516test_valid_only(RootDatum rd)

test

L539test(RootDatum rd,Partition P)

also in this file at line 495; also defined in test_unitarity.at, all_finite_order.at, nilpotent_centralizer.at

Generated from atlas-scripts at commit 7e1b958 (2026-09-17).