#### 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