Generalized Green functions associated to complex reflection groups
Representation Theory
2019-09-17 v2
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 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.
Keywords
Cite
@article{arxiv.1807.02677,
title = {Generalized Green functions associated to complex reflection groups},
author = {Toshiaki Shoji},
journal= {arXiv preprint arXiv:1807.02677},
year = {2019}
}
Comments
28 pages, final version, to appear in J. of Algebra