Structure Coefficients of the Hecke Algebra of (S2n,Bn)" role="presentation" style="font-size: 113%; position: relative;">(S2n,Bn)(S2n,Bn)(\mathcal{S}_{2n},\mathcal{B}_n)

SUMMARY

The Hecke algebra of the pair (S2n,Bn)(\mathcal{S}_{2n},\mathcal{B}_n), where Bn\mathcal{B}_n is the hyperoctahedral subgroup of S2n\mathcal{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 algebra which projects onto the Hecke algebra of (S2n,Bn)(\mathcal{S}_{2n},\mathcal{B}_n) for every nn. To build it, by using partial bijections we introduce and study a new class of finite dimensional algebras.