Omar Tout
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Structure coefficients of the Hecke algebra of (S2n,Bn)
dmtcs:2323 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2013,
DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
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https://doi.org/10.46298/dmtcs.2323
Structure coefficients of the Hecke algebra of (S2n,Bn)Conference paper
Authors: Omar Tout 1
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Omar Tout
1 Laboratoire Bordelais de Recherche en Informatique
The Hecke algebra of the pair (S2n,Bn), where Bn is the hyperoctahedral subgroup of S2n, was introduced by James in 1961. It is a natural analogue of the center of the symmetric group algebra. In this paper, we give a polynomiality property of its structure coefficients. Our main tool is a combinatorial universal algebra which projects on the Hecke algebra of (S2n,Bn) for every n. To build it, we introduce new objects called partial bijections.