Gindikin-Karpelevich finiteness for Kac-Moody groups over local fields

TL;DR

This paper establishes finiteness properties for split Kac-Moody groups over local non-archimedean fields, extending previous affine cases using the hovel structure as an analogue of Bruhat-Tits buildings.

Contribution

It generalizes Gindikin-Karpelevich finiteness results to non-affine Kac-Moody groups over local fields using the hovel framework.

Findings

Proves finiteness results for Kac-Moody groups over local fields.

Extends previous affine Gindikin-Karpelevich formulas.

Utilizes the hovel structure as an analogue of Bruhat-Tits buildings.

Abstract

In this paper, we prove some finiteness results about split Kac-Moody groups over local non-archimedean fields. Our results generalize those of "An affine Gindikin-Karpelevich formula" by Alexander Braverman, Howard Garland, David Kazhdan and Manish Patnaik. We do not require our groups to be affine. We use the hovel I associated to this situation, which is the analogue of the Bruhat-Tits building for a reductive group.