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

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

1995-08-18

arxiv.org/abs/math/9508203v1

Mathematics

Representation Theory

32 pages, Latex

Scientific paper

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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