Green Functions Associated to Complex Reflection Groups

Abstract

Green functions of classical groups are determined by the data from Weyl groups and by certain combinatorial objects called symbols. Generalizing this, we define Green functions associated to complex reflection groups G( e, 1, n) and study their combinatorial properties. We construct Hall–Littlewood functions and Schur functions in our scheme and show that such Green functions are obtained as a transition matrix between those two symmetric functions, as in the case of GL n .