exceptional.at

EllipticDatum type

set_type EllipticDatum = (WeylElt w,[int] charpoly, int order, int length, string name, int size)

Fields: w, charpoly, order, length, name, size

data type for table of elliptic conjugacy classes
could be expanded to all conjugacy classes

EllipticTable type

set_type EllipticTable=[EllipticDatum]

root_datum

table is assumed non-empty and all WeylElt are for same RootDatum

also in this file at line 63; also defined in basic.at, W_reps.at, K_Nilpotent.at, sommers.at, parabolics.at, K.at, nilpotent_orbits.at, W_classes.at, extended_misc.at, character_tables.at, springer_tables.at, disconnected.at, cyclotomic_Lie_algebra.at, bracket.at

lookup_by_name

also in this file at line 64

show

nice output of table

also in this file at line 75; also defined in modules.at, K_Nilpotent.at, good_W_representatives.at, arthur_parameters.at, sub_cells.at, associated_variety_annihilator.at, geck_generic.at, L_packet.at, ratmat.at, Levi_subgroups.at, nilpotent_orbits.at, subgroups.at, poset.at, cyclotomic.at, polynomial.at, character_tables.at, springer_tables.at, hodgeParamLaurentPol.at, hodgeParamPol.at, laurentPolynomial.at, weak_packets.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, nilpotent_posets.at, lazy_lists.at

show_long

include a representative of each class

also defined in character_tables.at, springer_tables.at, hodgeParamLaurentPol.at, hodgeParamPol.at, weak_packets.at, cyclotomic_Lie_algebra.at, bracket.at

NilpotentDatum type

set_type NilpotentDatum=(RootDatum root_datum,string name ,string alt_name,int special,[int] closure,string dual,string A,string Abar,[int] diagram)

Fields: root_datum, name, alt_name, special, closure, dual, A, Abar, diagram

data type for a table of information about nilpotent orbits

name: according to Carter
alt_name: Spaltenstein/Mizuno etc., when different
special: 1 or 0
closure: orbits in the closure (not including itself)
dual: name of dual orbit
A: string giving A(O)
Abar: Lusztig's quotient
diagram: labeled Dynkin diagram

orbit

also defined in springer_tables.at, W_reps_type_BC.at

dimension

also defined in basic.at, finite_dimensional.at, K_highest_weights.at, nilpotent_orbits.at, character_tables.at, W_reps_type_BC.at, tensor_product.at

is_special

also defined in combinatorics.at, springer_tables.at, W_reps_type_BC.at

is_even

also defined in basic.at, nilpotent_orbits.at

H

_of_triple

also defined in groups.at, cyclotomic_Lie_algebra.at, bracket.at

Levi

also defined in parabolics.at

is_distinguished

also defined in sommers.at, twisted_root_datum.at

NilpotentTable type

set_type NilpotentTable=[NilpotentDatum]

root_datum

also in this file at line 16; also defined in basic.at, W_reps.at, K_Nilpotent.at, sommers.at, parabolics.at, K.at, nilpotent_orbits.at, W_classes.at, extended_misc.at, character_tables.at, springer_tables.at, disconnected.at, cyclotomic_Lie_algebra.at, bracket.at

lookup_by_name

also in this file at line 18

lookup_by_alt_name

lookup_by_diagram

long_name 2 overloads

show

nice output

also in this file at line 22; also defined in modules.at, K_Nilpotent.at, good_W_representatives.at, arthur_parameters.at, sub_cells.at, associated_variety_annihilator.at, geck_generic.at, L_packet.at, ratmat.at, Levi_subgroups.at, nilpotent_orbits.at, subgroups.at, poset.at, cyclotomic.at, polynomial.at, character_tables.at, springer_tables.at, hodgeParamLaurentPol.at, hodgeParamPol.at, laurentPolynomial.at, weak_packets.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, nilpotent_posets.at, lazy_lists.at

nilpotent_poset

extract NilpotentPoset from the table

also defined in nilpotent_posets.at

closure

fill in all orbits in the closure of each given one (not just covering relations)

also defined in K_Nilpotent.at, poset.at

sub_table 2 overloads

extract table given by rows
the closure relations require work (throwing out terms and renumbering)

also defined in structure_constants.at

text_save

save a table in a form that can be read in by atlas

shift_closures_by_one

tool for fixing the closures, the source files numbered starting
at 1 not 0, this shouldn't be needed any more

graph

graph from a table, with specified labels

also in this file at line 159, line 167; also defined in poset.at, nilpotent_posets.at

preimage

given function from strings -> strings, find preimage

lusztig_graph

graph showing closure relations in the image of Lusztig's map from [W] to
N, restricted to elliptic elements

graph 2 overloads

graph of a nilpotent poset (see nilpotent_posets.at), using
the table for the names

also in this file at line 127; also defined in poset.at, nilpotent_posets.at

sub_table_distinguished

sub_table_even