nilpotent_posets.at

NilpotentPoset type

set_type NilpotentPoset =
  (RootDatum root_datum, [ComplexNilpotent] orbits, Poset orbit_closures)

Fields: root_datum, orbits, orbit_closures

list of complex orbits and their closure relations

nilpotent_poset

identity, for now

also defined in exceptional.at

sort

sort by dimension

also defined in sommers.at, sort.at, hodge_functions.at

find

also defined in basic.at, tits_centralizer.at, nilpotent_orbits.at, cells.at, K_types.at, hodgeParamLaurentPol.at, extended.at, disconnected.at, K_types_plus.at

eliminate_duplicates

sort_u

also defined in sort.at, K_types.at

saturate

saturate the orbits of L together with their closure relations

also defined in nilpotent_orbits.at, disconnected.at

merge

combine two complex nilpotent posets
P=(orbits_P,posets_P)
Q=(orbits_Q,posets_Q)
new_orbit: sort_u(orbits_P##orbits_Q)
new_posets: relations on new_orbits coming from posets_P and posets_Q

also defined in sort.at

submerge

variant of merge:
assuming: P.orbits\subset Q.orbits
application: Q is all orbits for rd (and some relations)
submerge adds the relations from P,
more efficient than using merge in this case

seed_complex_nilpotent_poset

seed with (list of complex nilpotents, trivial relations)
trivial relations:
0 < everything < principal

fill_nilpotent_posets_subregular

given poset of nilpotents, add the relations coming from the subregular orbits

fill_nilpotent_posets_minimal

given poset of nilpotents, add the relations coming from the minimal orbits

starting_complex_nilpotent_poset

starting point:
list of complex nilpotents
closure relations from 0 and principal orbits  (seed)
closure relations from subregular orbits (fill_nilpotent_posets_subregular)
closure relations from minimal orbits  (fill_nilpotent_posets_minimal)

nilpotent_orbits_and_closures

graph

graph of NilpotentPoset
this is the graph of the poset, together with labels
(H,dimension) from the orbits
see exceptional.at for a version using a NilpotentTable
for the names

also defined in poset.at, exceptional.at

special_elliptic

lusztig_of_special_elliptic 2 overloads

g

also defined in laurentPolynomial.at

sort_by_dimension_of_nilpotent

sort [WeylElt] by dimension of Lusztig(w) (associated nilpotent),
assuming each w is special elliptic so Lusztig(w) is known

special_elliptic_poset

master_complex_nilpotent_poset

nilpotent_orbits_and_closures_saturate

simple_induce

assume P is for a Levi

also defined in nilpotent_induction.at

nilpotent_orbits_and_closures_induce

test

also defined in test_unitarity.at, all_finite_order.at, nilpotent_centralizer.at, sommers.at, tensor_product.at

nilpotent_orbits_and_closures_test

for testing: just go up to N

show 2 overloads

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, exceptional.at, lazy_lists.at

show_subgroup_orbit_nilpotent_map