Timeline for Decomposition into irreducibles of the representation $L^2(SL_2(\mathbb{C})/\Gamma)$ for $\Gamma$ geometrically finite

10 events

when toggle format	what		by	license	comment
Dec 14, 2013 at 19:28	comment	added	Marc Palm		Just to be clear, the spherical part is infinite dimensional because $L^2(\Gamma \backslash G /K)$ is and the one-dimensional only a subspace of the spherical part. We don't know in general if the cuspidal part is infinite-dimensional, but only in the congruence setting (Weyl law).
Dec 14, 2013 at 19:27	history	edited	Marc Palm	CC BY-SA 3.0	added 204 characters in body
Dec 14, 2013 at 19:25	comment	added	Marc Palm		Yes, the one-dimensional representation is the trivial one and is spherical.
Dec 14, 2013 at 19:19	comment	added	user7894		The non-spherical part has no reason to be finite dimensional, has it ?
Dec 14, 2013 at 18:24	history	edited	Marc Palm	CC BY-SA 3.0	added 281 characters in body
Dec 14, 2013 at 17:38	history	edited	Marc Palm	CC BY-SA 3.0	added 422 characters in body
Dec 14, 2013 at 17:37	comment	added	Asaf		@PM, I'm given the impression that the OP asked about infinite-volume spectral theory.
Dec 14, 2013 at 17:31	history	edited	Marc Palm	CC BY-SA 3.0	added 422 characters in body
Dec 14, 2013 at 17:19	history	edited	Marc Palm	CC BY-SA 3.0	added 422 characters in body
Dec 14, 2013 at 17:12	history	answered	Marc Palm	CC BY-SA 3.0