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Descent sets for symplectic groups
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Rubey, Martin, Sagan, Bruce E. and Westbury, Bruce W. (2014) Descent sets for symplectic groups. Journal of Algebraic Combinatorics, Volume 40 (Number 1). pp. 187-208. doi:10.1007/s10801-013-0483-4 ISSN 0925-9899.
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Official URL: http://dx.doi.org/10.1007/s10801-013-0483-4
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 tensor products of the defining representation 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.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Algebraic Combinatorics | ||||
Publisher: | Springer New York LLC | ||||
ISSN: | 0925-9899 | ||||
Official Date: | 1 August 2014 | ||||
Dates: |
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Volume: | Volume 40 | ||||
Number: | Number 1 | ||||
Page Range: | pp. 187-208 | ||||
DOI: | 10.1007/s10801-013-0483-4 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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