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On Limit Multiplicities for Spaces of Automorphic Forms
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- Journal:
- Canadian Journal of Mathematics / Volume 51 / Issue 5 / 01 October 1999
- Published online by Cambridge University Press:
- 20 November 2018, pp. 952-976
- Print publication:
- 01 October 1999
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- Article
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Let
$\Gamma $ be a rank-one arithmetic subgroup of a semisimple Lie group 
$G$. For fixed 
$K$-Type, the spectral side of the Selberg trace formula defines a distribution on the space of infinitesimal characters of $G$, whose discrete part encodes the dimensions of the spaces of square-integrable $\Gamma $-automorphic forms. It is shown that this distribution converges to the Plancherel measure of $G$ when $\Gamma $ shrinks to the trivial group in a certain restricted way. The analogous assertion for cocompact lattices $\Gamma $ follows from results of DeGeorge-Wallach and Delorme.
