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Article Dans Une Revue Annals of Combinatorics Année : 2022

Diamond Cone for $${{\mathfrak {sl}}}(m,n)$$

Résumé

In this paper, we study the shape and the reduced shape algebra for the Lie superalgebra sl(m, n). We define quasistandard Young tableaux, and they give a combinatorial basis for the reduced shape algebra, called the diamond cone. There is a natural bijective map from the set of semistandard tableaux with shape lambda to the set of quasistandard tableaux with smaller shape: the diamond cone is compatible with the stratification of the reduced shape algebra.

Dates et versions

hal-03927660 , version 1 (06-01-2023)

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Boujemaâ Agrebaoui, Didier Arnal, Olfa Khlifi. Diamond Cone for $${{\mathfrak {sl}}}(m,n)$$. Annals of Combinatorics, 2022, 26 (2), pp.481-500. ⟨10.1007/s00026-021-00540-9⟩. ⟨hal-03927660⟩
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