Vol. 313, No. 1, 2021

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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
Authors
Kyu-Hwan Lee
Department of Mathematics
University of Connecticut
Storrs, CT
United States
Dongwen Liu
School of Mathematical Sciences
Zhejiang University
Hangzhou
China
Thomas Oliver
School of Mathematical Sciences
University of Nottingham
Nottingham
United Kingdom