Green functions associated to complex reflection groups, II

Abstract

Green functions associated to complex reflection groups G ( e ,1, n ) were discussed in the author's previous paper. In this paper, we consider the case of complex reflection groups W = G ( e , p , n ). Schur functions and Hall–Littlewood functions associated to W are introduced, and Green functions are described as the transition matrix between those two symmetric functions. Furthermore, it is shown that these Green functions are determined by means of Green functions associated to various G ( e ′,1, n ′). Our result involves, as a special case, a combinatorial approach to the Green functions of type D n .