Generators of the Hecke algebra of (S2n,BnS2n,Bn)

In analogy with the set of Jucys–Murphy elements, a set of ring generators for the Hecke algebra of the Gel’fand pair (S2n,Bn)(S2n,Bn), where BnBn is the hyperoctahedral subgroup of the symmetric group S2nS2n is constructed. Various consequences are presented, a conjecture of S. Matsumoto is proven.