• 1 Institut für Algebra, Zahlentheorie und Diskrete Mathematik
• 2 Fakultät für Mathematik und Geoinformation [Wien]
• 3 Department of Mathematics [Lansing]
• 4 Department of Mathematics, University of Warwick

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.