Relations between Kazhdan-Lusztig polynomials for real and p-adic groups

Abstract: We relate certain Kazhdan-Lusztig polynomials that arise in the representation theory of real and $p$-adic groups. The polynomials encode the multiplicity of irreducible representations in standard ones. In both, the real and p-adic setting, there are relevant geometric parameters that index both irreducible and standard modules. I will briefly review the geometric setting. Next, I will discuss earlier contributions by Zelevinski and by Ciubotaru-Trapa. In presenting new results, I will emphasize examples. I will explain how, under assumptions, these results imply that the decomposition matrix for a class of unipotent representation of split $p$-adic groups is a submatrix of the decomposition matrix of representations of split real groups.

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.