  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 multi-parameter Kostka
functions. As an application, we show that the generalized Green functions of
symplectic groups can be described combinatorially in terms of those
(one-parameter) Kostka functions.
