Bounds for multiplicities of unitary representations of cohomological type in spaces of cusp forms

Let $G_{\infty}$ be a semisimple real Lie group with unitary dual $\widehat{G}_{\infty}$ . We produce new upper bounds for the multiplicities with which representations $\pi \in \widehat{G}_{\infty}$ of cohomological type appear in certain spaces of cusp forms on $G_{\infty}$ . The main new idea is...

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Bibliographic Details
Published in:Annals of mathematics 2009-11, Vol.170 (3), p.1437-1446
Main Authors: Calegari, Frank, Emerton, Matthew
Format: Article
Language:English
Subjects:
Abstract spaces
Algebra
Arithmetic
Coefficients
Commutative rings and algebras
Exact sciences and technology
General mathematics
General, history and biography
Group theory
Integers
Lie groups
Logical theorems
Mathematical cusps
Mathematical rings
Mathematical theorems
Mathematics
Number theory
Sciences and techniques of general use
Topological groups, lie groups
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Summary:Let $G_{\infty}$ be a semisimple real Lie group with unitary dual $\widehat{G}_{\infty}$ . We produce new upper bounds for the multiplicities with which representations $\pi \in \widehat{G}_{\infty}$ of cohomological type appear in certain spaces of cusp forms on $G_{\infty}$ . The main new idea is to apply noncommutative Iwasawa theory to certain p-adic completions of the cohomology of locally symmetric spaces.
ISSN:0003-486X
1939-8980
DOI:10.4007/annals.2009.170.1437