Journal of Lie Theory

no. 4
On the Decomposition of L2(Γ \ G) in the Cocompact Case
Journal of Lie Theory, Volume 18 (2008) no. 4, pp. 937-949
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 $L^2(\Gamma\setminus G)$.
DOI: 10.5802/jolt.535
Classification: 22Exx, 11F03
Keywords: Poincare series, cocompact quotients 
@article{JOLT_2008_18_4_a12,
     author = {G. Muic},
     title = {On the {Decomposition} of {L\protect\textsuperscript{2}(\ensuremath{\Gamma}} \ {G)} in the {Cocompact} {Case}},
     journal = {Journal of Lie Theory},
     pages = {937--949},
     year = {2008},
     volume = {18},
     number = {4},
     doi = {10.5802/jolt.535},
     zbl = {1163.22005},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.535/}
}
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G. Muic. On the Decomposition of L2(Γ \ G) in the Cocompact Case. Journal of Lie Theory, Volume 18 (2008) no. 4, pp. 937-949. doi: 10.5802/jolt.535

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