Generalized Green functions associated to complex reflection groups

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 the multi-paramete...

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Bibliographic Details
Published inJournal of algebra Vol. 558; pp. 677 - 707
Main Author Shoji, Toshiaki
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.09.2020
Subjects
Complex reflection groups
Generalized Green functions
Hall-Littlewood functions
Kostka functions
r-Symbols
Symplectic groups
Kostka functions
Complex reflection groups
r-Symbols
Hall-Littlewood functions
Symplectic groups
Generalized Green functions
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Summary: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 the multi-parameter Kostka functions. As an application, we show that the generalized Green functions of symplectic groups can be described combinatorially in terms of our (one-parameter) Kostka functions.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2019.04.020