A comparison of Weyl group actions on Lagrangian cycles
type: Item
instance of: scholarly article
title: A comparison of Weyl group actions on Lagrangian cycles
zbMATH Open document ID: 0913.22008
DOI: 10.1016/S0019-3577(98)80015-3
author: Mladen Božičević
published in: Indagationes Mathematicae. New Series
publication date: 1999-05-30T00:00:00Z
review text: Let \(G\) be a connected complex reductive algebraic group. Write \(W\) for its Weyl group and \(X\) for its flag variety. In this paper, \(Q\) is any real closed Lie subgroup of \(G\) having finitely many orbits on \(X\). For such \(Q\), write \(T^*_Q(X)\) for the conormal variety of the \(Q\)-action. In this case, the cycles supported by \(T^*_Q(X)\) may be given a \(W\)-module structure (e.g., see Lusztig). Moreover, write \(D_Q^b(X)\) for the bounded derived category of sheaves on \(X\) whose characteristic variety is contained in \(T^*_Q(X)\). Then it is also true that the Grothendieck group \({\mathcal K}_Q(X)\) of \(D_Q^b(X)\) has a \(W\)-module structure given by intertwining operators. The main theorem of this paper proves the characteristic cycle and defines a homomorphism of \(W\)-modules mapping \({\mathcal K}_Q(X) \rightarrow H_{2n}(T^*_Q(X), {\mathbb C})\), where \(n=\dim_{\mathbb C}X\) and \(H_*(\cdot, {\mathbb C})\) is the Borel-Moore homology.
Mathematics Subject Classification ID: 22E41
zbMATH DE Number: 1251259
zbMATH Keywords: connected complex reductive algebraic group
zbMATH Keywords: Weyl group
zbMATH Keywords: flag variety
zbMATH Keywords: bounded derived category of sheaves
zbMATH Keywords: intertwining operators
zbMATH Keywords: Borel-Moore homology
reviewed by: Mark R. Sepanski
MaRDI profile type: Publication
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full work available at URL: s0019-3577(98)80015-3
OpenAlex ID: W1983584632
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description: scientific article; zbMATH DE number 1251259