Invariants for representations of Weyl groups and two-sided cells
type: Item
instance of: scholarly article
title: Invariants for representations of Weyl groups and two-sided cells
zbMATH Open document ID: 0928.20035
author: V. Pereyra
published in: Journal of the Mathematical Society of Japan
publication date: 1999-10-26T00:00:00Z
review text: The notion of two-sided cell, which was originally introduced by A.~Joseph and reformulated by D.~Kazhdan and G.~Lusztig, has played an important role in representation theory. Results concerning them have been obtained by very deep and sometimes ad hoc arguments. Here we introduce certain polynomial invariants for irreducible representations of Weyl groups. Our invariants are easily calculated, and the calculational results show that they almost determine the two-sided cells. Moreover, the factorization pattern of our polynomial invariants seems to be controlled by the natural parameter set \({\mathcal M}({\mathcal G})\) of each two-sided cell. Recently N.~Kawanaka introduced a new invariant, whose definition resembles the invariants studied in the present paper. We studied Kawanaka's invariants, and observed again a similar relation as above. This observation is discussed elsewhere.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 05A30
zbMATH DE Number: 1336905
zbMATH Keywords: irreducible representations of Weyl groups
zbMATH Keywords: two-sided cells
zbMATH Keywords: polynomial invariants
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/05110001
OpenAlex ID: W2052045213
DOI: 10.2969/JMSJ/05110001
description: scientific article; zbMATH DE number 1336905