Relating Arthur packets of real unitary groups and $p$-adic symplectic and orthogonal groups

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Deng, Taiwang, Huang, Chang, Xu, Bin, Zhao, Qixian
Format: Preprint
Published: 2026
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910056115601408
author Deng, Taiwang
Huang, Chang
Xu, Bin
Zhao, Qixian
author_facet Deng, Taiwang
Huang, Chang
Xu, Bin
Zhao, Qixian
contents We establish an explicit correspondence of certain Arthur packets between real unitary groups and $p$-adic symplectic or orthogonal groups. This allows one to compute Arthur packets of real unitary groups by translating results from the $p$-adic side. A main ingredient in our proof is an explicit relation between Zuckerman's translation functor on the real side and the Jacquet functor on the $p$-adic side. To achieve this, we construct a correspondence of stacks of Langlands parameters with fixed infinitesimal characters between the relevant real and $p$-adic groups. Our approach also allows one to relate the Kazhdan-Lusztig polynomials and the microlocal geometry between real and $p$-adic sides.
format Preprint
id arxiv_https___arxiv_org_abs_2603_16314
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Relating Arthur packets of real unitary groups and $p$-adic symplectic and orthogonal groups
Deng, Taiwang
Huang, Chang
Xu, Bin
Zhao, Qixian
Representation Theory
Number Theory
We establish an explicit correspondence of certain Arthur packets between real unitary groups and $p$-adic symplectic or orthogonal groups. This allows one to compute Arthur packets of real unitary groups by translating results from the $p$-adic side. A main ingredient in our proof is an explicit relation between Zuckerman's translation functor on the real side and the Jacquet functor on the $p$-adic side. To achieve this, we construct a correspondence of stacks of Langlands parameters with fixed infinitesimal characters between the relevant real and $p$-adic groups. Our approach also allows one to relate the Kazhdan-Lusztig polynomials and the microlocal geometry between real and $p$-adic sides.
title Relating Arthur packets of real unitary groups and $p$-adic symplectic and orthogonal groups
topic Representation Theory
Number Theory
url https://arxiv.org/abs/2603.16314