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

Abstract Let G∞ be a semisimple real Lie group with unitary dual Gˆ∞. We produce new upper bounds for the multiplicities with which representations π∈Gˆ∞ of cohomological type appear in certain spaces of cusp forms on G∞. The main new idea is to apply noncommutative Iwasawa theory to certain p-adic completions of the cohomology of locally symmetric spaces.

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数学年刊(Annals of Mathematics)

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