Seminar for Unitary Representations and Automorphic Forms

On Monday, February 3rd, 2024, 16:00 hours, Ekta Tiwari (University of Ottawa) will hold lecture titled:

Branching rules for irreducible supercuspidal representations of unramified U(1,1).

Abstract:

The study of branching rules involves examining how an irreducible repre- sentation breaks down when restricted to a specific subgroup. The aim is to uncover hidden internal symmetries within the original representation and to highlight shared features across related families of representations. As part of my Ph.D. thesis, I prove that for the rank-one quasi-split unramified unitary group G, the restriction of a supercuspidal representation of G(F) to a maximal compact subgroup K is multiplicity-free. I provide an explicit decomposition into irreducible representations of K characterized by unique depth and degree, something known only for two other groups (both of rank one).
Moreover, upon restriction to a smaller subgroup of K the decomposition can be described entirely using representations constructed from the nilpotent orbits of the Lie algebra of G(F), thus proving a new case of a novel recent conjecture in the literature.In this talk, I will introduce the foundational definitions, outline the branching problems under consideration, and finally present an explicit description of this decomposition for positive depth supercuspidal representations of G(F).

Lecture will be held via Zoom:
Time: Feb 3, 2025 16:00 Europe/Zagreb
Join Zoom Meeting
https://zoom.us/j/91594581259?pwd=hl61ObJdHSFSYJuZq1CJnrYW4DtNir.1

Meeting ID: 915 9458 1259
Passcode: 975798