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Automorphic representations and Harmonic analysis
Automorphic representations and Harmonic analysis
A correspondence of Arthur packets between real unitary groups and p-adic special odd orthogonal groups
A correspondence of Arthur packets between real unitary groups and p-adic special odd orthogonal groups
Organizers
Speaker
Bin Xu
Time
Wednesday, October 28, 2026 1:30 PM - 2:30 PM
Venue
A3-1a-205
Online
Zoom 787 662 9899
(BIMSA)
Abstract
We establish an explicit correspondence of certain Arthur packets between real unitary groups and p-adic special odd orthogonal groups. As an application, one can compute the Arthur packets of real unitary groups by translating the results from the p-adic side. The main feature of our proof is to relate the Zuckerman's translation functor on the real side with 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. It also allows us to relate the Kazhdan-Lusztig polynomials and the microlocal geometry between real and p-adic cases. This is joint work with Taiwang Deng, Chang Huang and Qixian Zhao.