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arXiv · 1303.5850

Descent sets for symplectic groups

Martin Rubey·Bruce Sagan·Bruce W. Westbury
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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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Martin Rubey, Bruce Sagan, Bruce W. Westbury. 2013-03-23. Descent sets for symplectic groups. https://arxiv.org/abs/1303.5850

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