We're sorry but this page doesn't work properly without JavaScript enabled. Please enable it to continue.
Feedback

Certain finiteness results for local Kac-Moody groups

00:00

Formal Metadata

Title
Certain finiteness results for local Kac-Moody groups
Title of Series
Number of Parts
7
Author
Contributors
License
CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Identifiers
Publisher
Release Date
Language

Content Metadata

Subject Area
Genre
Abstract
About half a century ago, Simon Gindikin and Fredrick Karpelevich evaluated the well known Harish Chandra’s \textbf{c}-function for semisimple Lie groups. This solution became known as the Gindikin-Karpelvich formula. While studying the constant term of Eisenstein series on adelic groups, Langland in \emph{Euler Products}, formulated the p-adic analogue of \textbf{c}-function and solved this integral. Macdonald independently obtained this formula for p-adic Chevalley groups in his lectures notes \emph{Spherical Functions on a Group of p-adic Type}. In Kac-Moody settings, which are infinite dimensional in general, the first challenge is to show that the algebraic analogue of the \textbf{c}-function is well defined. This can be done by proving certain finiteness results. For affine Kac-Moody groups, Braverman, Garland, Kazhdan, and Patnaik (BGKP) did this in 2014. Recently, Auguste H´ebert generalized these results by using the combinatorial objects called \emph{hovels} associated with Kac-Moody groups. We are trying to obtain these finiteness results using the algebraic methods motivated by the work of BGKP. In my talk, I will describe these results and share our progress on it.