Generalized Green functions associated to complex reflection groups

Abstract

In this paper, we consider the set of r-symbols in a full generality. We construct Hall-Littlewood functions and Kostka functions associated to those r-symbols. We also discuss a multi-parameter version of those functions. We show that there exists a general algorithm of computing the multi-parameter Kostka functions. As an application, we show that the generalized Green functions of symplectic groups can be described combinatorially in terms of our (one-parameter) Kostka functions.