Cohomology of G/P for classical complex Lie supergroups G and characters of some atypical G-modules
type: Item
instance of: scholarly article
title: Cohomology of G/P for classical complex Lie supergroups G and characters of some atypical G-modules
zbMATH Open document ID: 0667.14023
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74859
review text: We compute the unique nonzero cohomology group of a generic \(G^ 0\)- linearized locally free \({\mathcal O}_{G^ 0/P}\)-module, where \(G^ 0\) is the identity component of a complex classical Lie supergroup G and \(P\hookrightarrow G^ 0\) is an arbitrary parabolic subsupergroup. In particular we prove that for \(G\neq {\mathbb{P}}(m), S{\mathbb{P}}(m)\) this cohomology group is an irreducible \(G^ 0\)-module. As an application we generalize the character formula of typical irreducible \(G^ 0\)-modules to a natural class of atypical modules arising in this way.
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 4091655
zbMATH Keywords: cohomology group of quotient of classical Lie supergroup
author: Ivan Penkov
author: Vera Serganova
MaRDI profile type: Publication
OpenAlex ID: W2319724446
cites work: Q3905428
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DOI: 10.5802/AIF.1192
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4091655