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Jeu de taquin and diamond cone for Lie (super)algebras
Journal article   Open access  Peer reviewed

Jeu de taquin and diamond cone for Lie (super)algebras

Boujemaâ Agrebaoui, Didier Arnal and Abdelkader Ben Hassine
Bulletin des sciences mathématiques, Vol.139(1), pp.75-113
02/2015
DOI: https://doi.org/10.1016/j.bulsci.2014.08.004

Abstract

Jeu de taquin Orthosymplectic Lie superalgebra Quasistandard Young tableaux Semistandard Young tableaux
In this paper, we recall combinatorial basis for shape and reduced shape algebras of the Lie algebras gl(n), sp(2n) and so(2n+1). They are given by semistandard and quasistandard tableaux. Then we generalize these constructions to the case of the Lie superalgebra spo(2n,2m+1). The main tool is an extension of Schützenberger's jeu de taquin to these algebras.
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https://doi.org/10.1016/j.bulsci.2014.08.004View
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