Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 177

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

U. Bunke, M. Olbrich

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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