Graded characters of induced representations for real reductive Lie groups. I
type: Item
instance of: scholarly article
title: Graded characters of induced representations for real reductive Lie groups. I
zbMATH Open document ID: 0688.22002
DOI: 10.1016/0021-8693(89)90048-3
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Induced Harish-Chandra modules or modules in category \({\mathfrak o}'\) are studied in terms of corresponding mixed perverse sheaves equipped with Frobenius actions. This correspondence is used to compute the socle and cosocle filtrations in several situations. Indeed, in these instances there is a correspondence between socle or cosocle filtrations with the weight filtration of the corresponding sheaf. Using the weight filtration, an invariant, the graded character, is attached to these modules. Two induced modules having the same graded character are said to be weakly isomorphic. The weak isomorphism classes of principal series modules for R-split groups are shown to coincide with the isomorphism classes for the modules. Moreover a conjecture extending this to all principal series modules is discussed.
Mathematics Subject Classification ID: 22E47
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 20D30
zbMATH DE Number: 4127525
zbMATH Keywords: Harish-Chandra modules
zbMATH Keywords: mixed perverse sheaves
zbMATH Keywords: Frobenius actions
zbMATH Keywords: socle and cosocle filtrations
zbMATH Keywords: weight filtration
zbMATH Keywords: induced modules
zbMATH Keywords: graded character
zbMATH Keywords: weak isomorphism classes
zbMATH Keywords: principal series modules
Wikidata QID: Q115366233
author: Luis Casian
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90048-3
OpenAlex ID: W1980582800
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description: scientific article; zbMATH DE number 4127525