On multiplicity in restriction of tempered representations of $p$-adic groups

Kwangho Choiy

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arXiv · 1306.6118

On multiplicity in restriction of tempered representations of $p$-adic groups

Kwangho Choiy

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Abstract

We establish an equality between two multiplicities: one in the restriction of tempered representations of a $p$-adic group to its closed subgroup with the same derived group; and one occurring in their corresponding component groups in Langlands dual sides, so-called $\mathcal{S}$-groups, under working hypotheses about the tempered local Langlands conjecture and the internal structure of tempered $L$-packets. This provides a formula of the multiplicity for $p$-adic groups by means of dimensions of irreducible representations of their $\mathcal{S}$-groups.

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Kwangho Choiy. 2013-06-26. On multiplicity in restriction of tempered representations of $p$-adic groups. https://arxiv.org/abs/1306.6118

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