A remark on the irreducible characters and fake degrees of finite real reflection groups
type: Item
instance of: scholarly article
title: A remark on the irreducible characters and fake degrees of finite real reflection groups
zbMATH Open document ID: 0824.20038
DOI: 10.1007/BF01241138
published in: Inventiones Mathematicae
publication date: 1995-11-01T00:00:00Z
full work available at URL: https://eudml.org/doc/144284
review text: Beynon and Lusztig have shown that the fake degrees of almost all irreducible characters of finite real reflection groups are palindromes, and that the exceptions to this rule correspond to the nonrational characters of the generic ring \(A\) defined over \(R=\mathbb{C}[q]\). Their proof consists of a case-by-case check. In this note we give an explanation for this phenomenon and some related facts about fake degrees. Moreover, in the situation where we allow for distinct parameters \(q_ \alpha\) in the definition of \(A\), we give a simple uniform proof of the fact that all the central idempotents of \(A^{\overline {K}}\) are elements of \(A^{\widetilde {K}}\), where \(\widetilde{K}=\mathbb{C}[\sqrt{q_ \alpha}]\).
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 20H15
zbMATH DE Number: 784011
zbMATH Keywords: characters of generic rings
zbMATH Keywords: fake degrees
zbMATH Keywords: irreducible characters
zbMATH Keywords: finite real reflection groups
zbMATH Keywords: palindromes
zbMATH Keywords: central idempotents
author: Eric Opdam
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 784011