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Article Dans Une Revue Algebras and Representation Theory Année : 2018

Sliding Presentation of the Jeux de Taquin for Classical Lie Groups

Résumé

The simple $GL(n,\mathbb {C})$-modules are described by using semistandard Young tableaux. Any semistandard skew tableau can be transformed into a well defined semistandard tableau by a combinatorial operation, the Schützenberger jeu de taquin. Associated to the classical Lie groups $SP(2n,\mathbb {C})$, $SO(2n+1,\mathbb {C})$, there are other notions of semistandard Young tableaux and jeux de taquin. In this paper, we study these various jeux de taquin, proving that each of them has a simple and explicit formulation as a step-by-step sliding. Any of these jeux de taquin is the restriction of the orthogonal one, associated to $SO(2n+1,\mathbb {C})$.
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Dates et versions

hal-01692930 , version 1 (25-01-2018)

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Didier Arnal, Olfa Khlifi. Sliding Presentation of the Jeux de Taquin for Classical Lie Groups. Algebras and Representation Theory, 2018, 21 (1), pp.219-237. ⟨10.1007/s10468-017-9711-2⟩. ⟨hal-01692930⟩
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