The p-adic Kazhdan-Lusztig hypothesis, generic representations, and orbits of smooth closure

Abstract: Building on the work of Zelevisnky and the cases for real and complex groups, Davis Vogan purposed a p-adic Kazhdan-Lusztig hypothesis: The dimensions of stalks of perverse sheaves on certain varieties of Langlands parameters, should coincide with multiplicities of irreducible representations of in "standard" representations. Moreover, Vogan defined what we call ABV-packets in terms of the microlocal geometry of the varieties of Langlands parameters, and purposed that these coincide with Arthur's A-packets.

We will discuss recent work which, under the assumption of the p-KLH, proves (various cases of) a conjecture of Gross-Prasad that an L-packet contains a generic representation if and only if the associated adjoint L-function is regular at s=1. We will also explore implications for Shahidi's enhanced genericity conjecture, an analogue for ABV-packets, and the role of orbits with smooth closure.

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.