\Gamma-Cohomology and the Selberg Zeta Function

Contents 1 Introduction 1 2 Acyclicity Lemmas 4 3 Resolutions of admissible representations 8 4 n-cohomology 11 5 \Gamma-cohomology 15 6 \Gamma-cohomology of the principal series 16 1 Introduction Let G be a semisimple Lie group of real rank one, K ae G be a maximal compact subgroup and g = k \Phi p be the Cartan decomposition of the Lie algebra g of G. Let a ae p be a one-dimensional subspace and M ae K be the centralizer of a in K. Fixing a positive root system of (g; a) we have the Iwasawa decomposition g = k \Phi a \Phi n. Let (oe; V oe ) 2 M be an irredu