2013/03/23 by Martin Rubey, Rubey, Martin, Bruce E. Sagan +3
Mathematics · #05E05 #05E10 #20C15 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1303.5850
openalex publication_date 2013/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.