# Principal series representations of Iwahori-Hecke algebras for Kac-Moody groups over local fields

## TL;DR

This paper introduces principal series representations for Iwahori-Hecke algebras associated with Kac-Moody groups over local fields, extending existing irreducibility criteria and deepening understanding of their structure.

## Contribution

It is the first to define and analyze principal series representations for these algebras, generalizing key irreducibility results.

## Key findings

- Partial generalization of Kato and Matsumoto irreducibility criteria
- Introduction of principal series representations for Kac-Moody Iwahori-Hecke algebras
- Enhanced understanding of the algebraic structure of these representations

## Abstract

Recently, Iwahori-Hecke algebras were associated to Kac-Moody groups over non-Archimedean local fields. We introduce principal series representations for these algebras. We study these representations and partially generalize Kato and Matsumoto irreducibility criteria.