Seminars & Colloquia Calendar

 Abstract:  One of the main difficulties in extending Macdonald’s theory of spherical functions from p-adic Chevalley groups to p-adic Kac-Moody groups is the absence of Haar measure in the infinite dimensional case. Related to this problem is the question of how to generalize the integral defining Harish-Chandra’s c-function to the p-adic Kac-Moody setting. These questions are answered by proving the Approximation Theorem, which is a formal analogue of Harish-Chanda's limit relating spherical and c-fucntion, and two certain finiteness’. We call these finiteness results the Gindikin-Karpelevich Finiteness and the Spherical Finiteness. In this talk, we will present the proofs of these results for infinite dimensional local Kac-Moody groups.

This work was completed under the supervision of Manish M. Patnaik.