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Lie Group Quantum Mathematics Seminar

Gindikin-Karpelevich Finiteness for Local Kac-Moody Groups

Abid Ali, MacEwan University

Location:  Hill 705
Date & time: Friday, 15 November 2019 at 12:00PM - 1:00PM

 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.

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