Geodesic
Descent sets for symplectic groups
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 1, pp. 187-208.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The descent set of an oscillating (or up-down) tableau is introduced. This descent set plays the same role in the representation theory of the symplectic groups as the descent set of a standard tableau plays in the representation theory of the general linear groups. In particular, we show that the descent set is preserved by Sundaram's correspondence. This gives a direct combinatorial interpretation of the branching rules for tensor products of the defining representation of the symplectic groups; equivalently, for the Frobenius character of the action of a symmetric group on an isotypic subspace in a tensor power of the defining representation of a symplectic group.
Classification : 05E10, 05E15, 20G05
Keywords: descent set, growth diagram, representations, symmetric functions, quasisymmetric functions, Young tableau 
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     title = {Descent sets for symplectic groups},
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Rubey, Martin; Sagan, Bruce E.; Westbury, Bruce W. Descent sets for symplectic groups. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 1, pp. 187-208. http://geodesic.mathdoc.fr/item/JAC_2014__40_1_a5/