Supercuspidal representations arising from stable vectors

Britain Cox, Purdue University

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 ∈ g a arise only when a is coprime to m. Given a stable vector v ∈ g a, we construct packets of supercuspidal representations π v,ρ as well as discrete Langlands parameters ϕ v. Both the parameter and representations are of depth a/m. We further show that for a fixed vector, π v,ρ and ϕv satisfy both sides of the formal degree conjecture.

Degree

Ph.D.

Advisors

Shahidi, Purdue University.

Subject Area

Mathematics

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