Analysis on Symmetric and Locally Symmetric Spaces (Multiplicities, Cohomology and Zeta functions)

2005/08/29 by Ulrich Bunke, Bunke, Ulrich, Robert Waldmueller +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Representation Theory (math.RT) #math.DG #math.RT

paper · pdf · doi:10.48550/arxiv.math/0508560

11 pages, Notes of a course given at the Summer School "Algebraic Groups" in Goettingen, June 27 - July 15

arxiv created 2005/08/29 · openalex publication_date 2005/08/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The goal of the course was a review of results mainly due to M. Olbrich and the first author. We consider a discrete cocompact subgroup Γ of a semisimple Lie group G. We relate the group cohomology of Γ with coefficients in the maximal globalization of a representation of G with the multiplicities of unitary representations of G in L²(G/Γ). Explicit calculations are given in the case G=SL(2,R). In the rank-one case we state a version of the Selberg trace formula, discuss the singularities of the Selberg zeta-functions, and state their relation with the cohomology of Γ in principal series representations.

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