
Journal of Lie Theory 18 (2008), No. 4, 937949 Copyright Heldermann Verlag 2008 On the Decomposition of L^{2}(Γ \ G) in the Cocompact Case Goran Muic Dept. of Mathematics, University of Zagreb, Bijenicka 30, 10000 Zagreb, Croatia gmuic@math.hr [Abstractpdf] Let $G$ be a semisimple Lie group with a finite center and finitely many connected components. For example, $G$ could be a group of $\mathbb R$points of a semisimple Zariski connected algebraic group defined over $\mathbb Q$. Let $\Gamma$ be a discrete cocompact subgroup of $G$. Using the spectral decomposition of compactly supported Poincar\' e series we discuss the existence of various types of irreducible unitary subrepresentations of $L^2(\Gamma\setminus G)$. Keywords: Poincare series, cocompact quotients. MSC: 22Exx, 11F03 [ Fulltextpdf (206 KB)] for subscribers only. 