SUPERCUSPIDAL REPRESENTATIONS ARISING FROM STABLE VECTORS

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 \{π_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, π_v,\rho and \varphi_v satisfy both sides of the formal degree conjecture.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2015

Author dc:creator

• Cox, Britain

Contributors dc:contributor

• Jiu-Kang Yu
• Freydoon Shahidi
• Tong Liu
• David Goldberg

Repository record dc:identifier

https://docs.lib.purdue.edu/open_access_dissertations/1346

OAI identifier oai:identifier

oai:docs.lib.purdue.edu:open_access_dissertations-2562