Unitary representations and a general vanishing theorem for \((0,r)\)- cohomology
type: Item
instance of: scholarly article
title: Unitary representations and a general vanishing theorem for \((0,r)\)- cohomology
zbMATH Open document ID: 0751.22004
author: Floyd L. Williams
published in: Osaka Journal of Mathematics
publication date: 1992-06-25T00:00:00Z
review text: A general and precise vanishing theorem for the \((0,r)\)-cohomology of a compact arithmetic quotient of a Hermitian symmetric space \(X=G/K\) (\(G\) a connected non-compact semisimple Lie group) is given. Moreover, the unitary representations of \(G\) which contribute via Matsushima's formula to these cohomology groups are described. These results improve the ones given by the author in his earlier paper [Osaka J. Math. 18, 147-160 (1981; Zbl 0469.32011)].
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 11F75
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 5693
zbMATH Keywords: vanishing theorem
zbMATH Keywords: Hermitian symmetric space
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: unitary representations
zbMATH Keywords: cohomology groups
reviewed by: Joachim Schwermer
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5693