Algebras and Representation Theory

, Volume 21, Issue 1, pp 219–237 | Cite as

Sliding Presentation of the Jeux de Taquin for Classical Lie Groups

  • Didier ArnalEmail author
  • Olfa Khlifi


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 \(SO(2n+1,\mathbb {C})\).


Jeu de taquin Semistandard young tableaux Classical lie groups 

Mathematics Subject Classification (2010)

17B20 05E10 05E15 


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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Institut de Mathématiques de Bourgogne, UMR CNRS 5584Université de Bourgogne Franche ComtéDijon CedexFrance
  2. 2.Unité de recherche UR 09-06, Faculté des SciencesUniversité de SfaxSfaxTunisie

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