Benkart-Kang-Kashiwara crystals for the general-linear Lie superalgebra

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