Some explicit descriptions of characters stabilizing smooth complex representations of GL(r, D) with a p-adic division algebra D

Author

Maryam Saeed Alzahrani, Southern Illinois University CarbondaleFollow

Date of Award

12-1-2025

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Choiy, Kwangho

Abstract

For a positive integer r and a central division algebra D over a non-archimedean field F of characteristic zero, we provide an explicit and precise description of (the number of) characters that stabilize irreducible smooth complex representations of GL(r,D). The works of Gelbart-Knapp and Hiraga-Saito on L-packets for inner forms of SL(n) over the p-adic field are being mainly applied, and we also explicitly discuss that there are some representations that have multiplicity that are different than 1.