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.
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
Date of Award
January 2015
Recommended Citation
Cox, Britain, "SUPERCUSPIDAL REPRESENTATIONS ARISING FROM STABLE VECTORS" (2015). Open Access Dissertations. 1346.
https://docs.lib.purdue.edu/open_access_dissertations/1346
First Advisor
Jiu-Kang Yu
Second Advisor
Freydoon Shahidi
Committee Member 1
Tong Liu
Committee Member 2
David Goldberg