Character expansion of Kac–Moody correction factors

Kyu-Hwan Lee, Dongwen Liu and Thomas Oliver

Vol. 313 (2021), No. 1, 159–183

DOI: 10.2140/pjm.2021.313.159

Abstract

A correction factor naturally arises in the theory of $p$-adic Kac–Moody groups. 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.

Keywords

Kac–Moody algebras, Weyl groups, Poincare series, Macdonald identity, correction factor, character expansions, Coxeter groups

Mathematical Subject Classification 2010

Primary: 17B22, 17B67

Secondary: 05E10

Milestones

Received: 22 February 2020

Revised: 30 April 2021

Accepted: 12 June 2021

Published: 17 September 2021