Diamond Cone for sl(m,n)

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 ta...

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Bibliographic Details
Published in:Annals of combinatorics 2022-06, Vol.26 (2), p.481-500
Main Authors: Agrebaoui, Boujemaâ, Arnal, Didier, Khlifi, Olfa
Format: Article
Language:English
Subjects:
Algebra
Combinatorial analysis
Combinatorics
Diamonds
Mathematics
Mathematics and Statistics
Online Access:Get full text
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Summary: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 λ to the set of quasistandard tableaux with smaller shape: the diamond cone is compatible with the stratification of the reduced shape algebra.
ISSN:0218-0006
0219-3094
DOI:10.1007/s00026-021-00540-9