Kato's irreducibility criterion for Kac-Moody groups over local fields

TL;DR

This paper extends Kato's irreducibility criterion from reductive groups to Kac-Moody groups over local fields, providing a key theoretical advancement in understanding their principal series representations.

Contribution

We prove Kato's irreducibility criterion for principal series representations of Kac-Moody groups over local fields, completing previous partial results.

Findings

Established irreducibility criterion for Kac-Moody groups

Extended Kato's criterion from reductive to Kac-Moody case

Provided theoretical foundation for principal series representations

Abstract

In 2014, Braverman, Kazhdan, Patnaik and Bardy-Panse, Gaussent and Rousseau associated Iwahori-Hecke algebras to Kac-Moody groups over non-Archimedean local fields. In a previous paper, we defined and studied their principal series representations. In 1982, Kato provided an irreducibility criterion for these representations, in the reductive case. We had obtained partially this criterion in the Kac-Moody case. In this paper, we prove this criterion in the Kac-Moody case.