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

Kwangho Choiy

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

Number Theory 2018-05-10 v6 Representation Theory

Authors: Kwangho Choiy

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.

Keywords

tempered representations $p$-adic groups restriction multiplicity Langlands dual $\mathcal{S}$-groups $L$-packets

Cite

@article{arxiv.1306.6118,
  title  = {On multiplicity in restriction of tempered representations of $p$-adic groups},
  author = {Kwangho Choiy},
  journal= {arXiv preprint arXiv:1306.6118},
  year   = {2018}
}

Comments

This present version supersedes arXiv:1306.6118v1-v5 -- changed the title; modified considerable parts of the manuscript; removed some sections. Accepted for publication in Mathematische Zeitschrift

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

Abstract

Keywords

Cite

Comments

Related papers