# Sliding Presentation of the Jeux de Taquin for Classical Lie Groups

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Abstract : 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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https://hal.archives-ouvertes.fr/hal-01692930
Contributor : Imb - Université de Bourgogne <>
Submitted on : Thursday, January 25, 2018 - 3:42:28 PM
Last modification on : Sunday, June 2, 2019 - 5:48:02 PM

### Citation

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

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