A symplectic jeu de taquin bijection between the tableaux of King and of De Concini

Sheats, Jeffrey

doi:10.1090/S0002-9947-99-02166-2

A symplectic jeu de taquin bijection between the tableaux of King and of De Concini
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by Jeffrey T. Sheats PDF

Trans. Amer. Math. Soc. 351 (1999), 3569-3607 Request permission

Abstract:

The definitions, methods, and results are entirely combinatorial. The symplectic jeu de taquin algorithm developed here is an extension of Schützenberger’s original jeu de taquin and acts on a skew form of De Concini’s symplectic standard tableaux. This algorithm is used to construct a weight preserving bijection between the two most widely known sets of symplectic tableaux. Anticipated applications to Knuth relations and to decomposing symplectic tensor products are indicated.

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