Generators of the Hecke algebra of (S _(2n), B _n)

摘要

In analogy with the set of Jucys-Murphy elements, a set of ring generators for the Hecke algebra of the Gel'fand pair (S _(2n), B _n), where B n is the hyperoctahedral subgroup of the symmetric group S _(2n) is constructed. Various consequences are presented, a conjecture of S. Matsumoto is proven.