Date of Award
January 2015
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Jiu-Kang Yu
Second Advisor
Freydoon Shahidi
Committee Member 1
Tong Liu
Committee Member 2
David Goldberg
Abstract
For a reductive group $G$ over a $p$-adic field $k$, one may grade the associated Lie algebra $\g$ by an automorphism of order $m$. It has been shown that stable vectors $v\in\g_{a}$ arise only when $a$ is coprime to $m$. Given a stable vector $v\in\g_{a}$, we construct packets of supercuspidal representations $\{\pi_{v,\rho}\}$ as well as discrete Langlands parameters $\varphi_{v}$. Both the parameter and representations are of depth $a/m$. We further show that for a fixed vector, $\pi_{v,\rho}$ and $\varphi_{v}$ satisfy both sides of the formal degree conjecture.
Recommended Citation
Cox, Britain, "SUPERCUSPIDAL REPRESENTATIONS ARISING FROM STABLE VECTORS" (2015). Open Access Dissertations. 1346.
https://docs.lib.purdue.edu/open_access_dissertations/1346