# Descent sets for oscillating tableaux

Abstract : 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 the defining representations 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.
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Conference papers

https://hal.inria.fr/hal-01229726
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dmAS0109.pdf
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• HAL Id : hal-01229726, version 1

### Citation

Martin Rubey, Bruce E. Sagan, Bruce W. Westbury. Descent sets for oscillating tableaux. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.97-108. ⟨hal-01229726⟩

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