Institution: | 1.Institut de Mathématiques de Bourgogne, UMR CNRS 5584,Université de Bourgogne Franche Comté,Dijon Cedex,France;2.Unité de recherche UR 09-06, Faculté des Sciences,Université de Sfax,Sfax,Tunisie |
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 \(SO(2n+1,\mathbb {C})\). |