Character expansion of Kac-Moody correction factors

TL;DR

This paper develops a character expansion for correction factors in p-adic Kac-Moody groups, providing explicit formulas for coefficients and showing they are polynomials in certain cases, advancing understanding of these algebraic structures.

Contribution

It introduces a novel character expansion of correction factors and derives explicit formulas for the coefficients, including their polynomial nature in specific cases.

Findings

Coefficients lie in the ring of power series with integral coefficients.

In the universal Coxeter group case, coefficients are polynomials.

Provides a new perspective on the structure of correction factors in Kac-Moody theory.

Abstract

A correction factor naturally arises in the theory of p-adic Kac--Moody groups. In this paper, we expand the correction factor into a sum of irreducible characters of the underlying Kac--Moody algebra. We derive a formula for the coefficients, which lie in the ring of power series with integral coefficients. In the case that the Weyl group is a universal Coxeter group, we show that the coefficients are actually polynomials.