Structure coefficients of the Hecke algebra of (S2n,Bn)
Abstract
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.
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