Cohomological properties of the smooth globalization of a Harish-Chandra module

1995/08/18 by Ulrich Bunke, U. Bunke, Bunke, U. +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Representation Theory (math.RT) #math.DG #math.RT

paper · pdf · doi:10.48550/arxiv.math/9508203

32 pages, Latex

arxiv created 1995/08/18 · openalex publication_date 1995/08/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the finiteness of the cohomology of torsion-free lattices in a semisimple Lie group of real rank one with coefficients in the distribution vector globalization of Harish-Chandra modules. The cohomology is expressed in terms of automorphic and cusp forms. We also consider the Lie-algebra cohomology of these globalizations for the nilpotent part of the Iwasawa decomposition of the group.

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