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

Choiy, Kwangho

doi:10.1007/s00209-018-2091-4

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

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Choiy, Kwangho
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00209-018-2091-4
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Choiy, K. (2019). On multiplicity in restriction of tempered representations of p-adic groups. Mathematische Zeitschrift, 291(1-2), 449-471. doi:10.1007/s00209-018-2091-4.

Cite as: https://hdl.handle.net/21.11116/0000-0004-41A6-7

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
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 S -groups.