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Journal of Lie Theory 18 (2008), No. 4, 937--949
Copyright Heldermann Verlag 2008

On the Decomposition of L2(Γ \ G) in the Cocompact Case

Goran Muic
Dept. of Mathematics, University of Zagreb, Bijenicka 30, 10000 Zagreb, Croatia


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

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