On the finiteness of the \(L^ 2\)-automorphic cohomology of a flag domain
type: Item
instance of: scholarly article
title: On the finiteness of the \(L^ 2\)-automorphic cohomology of a flag domain
zbMATH Open document ID: 0622.32022
DOI: 10.1016/0022-1236(87)90079-6
author: Floyd L. Williams
published in: Journal of Functional Analysis
publication date: 1987-01-01T00:00:00Z
review text: Let \(D=G/V\) be a flag domain and let \(E_{\pi}\to D\) be a non-degenerate homogeneous vector bundle over D induced by an irreducible representation \(\pi\) of V. If \(\Gamma\subset G\) is a lattice we prove that the \((L^ 2- \Gamma)\)-automorphic cohomology of D with coefficients in \(E_{\pi}\) is finite dimensional. In particular we establish finiteness of \(\Gamma\)- automorphic cohomology of the period matrix domain \(D=S0_ 1(2n,1)/U(n)\). The finiteness question, which heretofore has been open, is posed by \textit{R. O. Wells} jun. and \textit{J. A. Wolf} [Ann. Math., II. Ser. 105, 397-448 (1977; Zbl 0448.32015)].
Mathematics Subject Classification ID: 32M10
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 32N10
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 32G20
zbMATH DE Number: 4008815
zbMATH Keywords: semi-simple Lie group
zbMATH Keywords: flag domain
zbMATH Keywords: homogeneous vector bundle
zbMATH Keywords: automorphic cohomology
zbMATH Keywords: period matrix
MaRDI profile type: Publication
full work available at URL: 0022-1236(87)90079-6
OpenAlex ID: W2062770022
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description: scientific article; zbMATH DE number 4008815