On Eisenstein series and the cohomology of arithmetic groups
type: Item
instance of: scholarly article
title: On Eisenstein series and the cohomology of arithmetic groups
zbMATH Open document ID: 1203.11043
author: Neven Grbac
author: Joachim Schwermer
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2010-07-20T00:00:00Z
review text: Automorphic cohomology of a reductive \(\mathbb Q\) group \(G\) is defined as the Lie-algebra cohomology of the space of automorphic forms (twisted by a finite dimensional representation). It is known to decompose as a direct sum over all classes of parabolic subgroups \(P\) according to the cuspidal support. The contributions for \(P\neq G\) can be constructed as residues or principal values of derivatives of Eisenstein series, which justifies the name \textit{Eisenstein cohomology} given to these contributions. The main result of the paper, spelled out for \(\mathbb Q\)-split groups, is that a given evaluation point can only contribute non-trivially to the cohomology, if its coordinates are half-integral, i.e., lie in \(\frac12\mathbb Z\). The proof, which is not given, rests on combinatorial descriptions of the parameter sets for the classical groups, which yield explicit formulae for the Weyl group actions.
reviewed by: Anton Deitmar
Mathematics Subject Classification ID: 11F75
zbMATH DE Number: 5757866
zbMATH Keywords: Automorphic cohomology
zbMATH Keywords: reductive group
MaRDI profile type: Publication
full work available at URL: j.crma.2010.04.007
OpenAlex ID: W2041793447
cites work: Harmonic analysis in weighted L2-spaces
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DOI: 10.1016/J.CRMA.2010.04.007
description: scientific article; zbMATH DE number 5757866