Quiver varieties and Weyl group actions
type: Item
instance of: scholarly article
title: Quiver varieties and Weyl group actions
zbMATH Open document ID: 0958.20036
author: G. Lusztig
publication date: 2000-05-17T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75426
review text: For a finite graph of type \(ADE\) with set of vertices \(I\), \textit{H.~Nakajima} associated to \(\mathbf{v,w}\in\mathbb{N}^I\) a ``quiver variety'' \(\mathcal M(\mathbf{v,w})\) and constructed a Weyl group action on the cohomology of \(\sqcup_{\mathbf v}\mathcal M(\mathbf{v,w})\) using techniques of hyper-Kähler geometry [see Duke Math. J. 76, No. 2, 365-416 (1994; Zbl 0826.17026), Duke J. Math. 91, No. 3, 515-560 (1998)]. In the paper under review it is given an alternative construction of this Weyl group action, based not on hyper-Kähler geometry, but on techniques of intersection cohomology. This gives in fact a refinement of the Weyl group action.
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 1448497
zbMATH Keywords: quiver varieties
zbMATH Keywords: Weyl groups
zbMATH Keywords: intersection cohomology
zbMATH Keywords: Weyl group actions
reviewed by: Vladimir L. Popov
MaRDI profile type: Publication
OpenAlex ID: W2324836681
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cites work: Quiver varieties and Kac-Moody algebras
DOI: 10.5802/AIF.1762
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1448497