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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Presented by Peter Littelmann.
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Arnal, D., Khlifi, O. Sliding Presentation of the Jeux de Taquin for Classical Lie Groups. Algebr Represent Theor 21, 219–237 (2018). https://doi.org/10.1007/s10468-017-9711-2
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DOI: https://doi.org/10.1007/s10468-017-9711-2