Benkart-Kang-Kashiwara crystals for the general-linear Lie superalgebra¶
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sage.combinat.crystals.bkk_crystals.
CrystalOfBKKTableaux
¶ Crystal of tableaux for type \(A(m|n)\).
This is an implementation of the tableaux model of the Benkart-Kang-Kashiwara crystal [BKK2000] for the Lie superalgebra \(\mathfrak{gl}(m+1,n+1)\).
INPUT:
ct
– a super Lie Cartan type of type \(A(m|n)\)shape
– shape specifying the highest weight; this should be a partition contained in a hook of height \(n+1\) and width \(m+1\)
EXAMPLES:
sage: T = crystals.Tableaux(['A', [1,1]], shape = [2,1]) sage: T.cardinality() 20