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 unram-
ified 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 de-
composition 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 branch-
ing problems under consideration, and finally present an explicit description of
this decomposition for positive depth supercuspidal representations of G(F).

 

 

Predavanje će se moći pratiti putem platforme 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
  

Pozivaju se članovi seminara i svi zainteresirani.

 

Marcela Hanzer