Desiderata and Uniqueness of the Local Langlands Correspondence

Abstract: The local Langlands conjecture predicts a "canonical" bijection between the set of smooth irreducible representations of a p-adic reductive algebraic group G and the set of enhanced L-parameter of G, known as the local Langlands correspondence (LLC). There are several constructions of LLC, either on specific types of groups or on special classes of representations. The comparison between different constructions of LLC is a non-trivial problem. In this talk, I will introduce a list of desiderata of LLC for general quasi-split p-adic group G. Then, I will show that when p is sufficiently large, the LLC that satisfies these desiderata is unique (if it exists). This is a joint work with Tasho Kaletha and Cheng-Chiang Tsai.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Canadian Rockies Representation Theory

Series comments: Topics include, but are not limited to, geometric and categorical aspects of the Langlands Programme. Please write to Jose Cruz for zoom instructions.