Martin Rubey ; Bruce E. Sagan ; Bruce W. Westbury - Descent sets for oscillating tableaux

dmtcs:12796 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.12796
Descent sets for oscillating tableauxArticle

Authors: Martin Rubey 1,2; Bruce E. Sagan 3; Bruce W. Westbury 4

  • 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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: oscillating tableaux,quasisymmetric expansion,Frobenius character,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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