English

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

R2 v1 2026-06-23T02:53:39.255Z