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arXiv · 1212.5375

Structure coefficients of the Hecke algebra of $(S_{2n},B_n)$

Omar Tout
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Abstract

The Hecke algebra of the pair $(S_{2n},B_n)$, where $B_n$ is the hyperoctahedral subgroup of $S_{2n}$, 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 $(S_{2n},B_n)$ for every $n$. To build it, we introduce new objects called partial bijections.

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Omar Tout. 2014-03-03. Structure coefficients of the Hecke algebra of $(S_{2n},B_n)$. https://doi.org/10.37236/3592

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