Green functions attached to limit symbols

Abstract

Hall-Littlewood functions and Green functions associated to complex reflection groups $W = G(r, 1, n)$ were constructed in [S1] by means of symbols, which are a generalization of partitions. In this paper, we consider such functions in the case where the symbols are of very special type, called "limit symbols". The situation becomes simple, and is close to the case of symmetric groups when the symbols tends to the "limit". In the case where $W$ is a Weyl group of type $B_n$, we give a closed formula for Hall-Littlewood functions, and verify some of the conjectures stated in [S1] for the case of Green functions attached to limit symbols.