FINITE GROUPS WITH MULTIPLICITY-FREE PERMUTATION CHARACTERS

摘要

Let G be a finite group and H a subgroup of G. The Hecke algebra H(G,H) associated with G and H is defined by the endomorphism algebra EndC[G]((CH)G), where CH is the trivial C[H]-module and (CH)G = CH direct X C[H] C[G]. As is well known, H(G,H) is a semisimple C-algebra and it is commutative if and only if (?H)G is multiplicity-free. In [6], by a ring theoretic method, it is shown that if the canonical involution of H(G,H) is the identity then H(G,H) is commutative and, if there exists an abelian subgroup A of G such that G = AH then H(G,H) is commutative. In this paper, by a character theoretic method, we consider the commutativity of H(G,H).