Character expansion of Kac–Moody correction factors

Lee, K.-H., Liu, D and Oliver, T. 2021. Character expansion of Kac–Moody correction factors. Pacific Journal of Mathematics. 313 (1), pp. 159-183. https://doi.org/10.2140/pjm.2021.313.159

TitleCharacter expansion of Kac–Moody correction factors
TypeJournal article
AuthorsLee, K.-H., Liu, D and Oliver, T.
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.

KeywordsKac–Moody algebras
Weyl groups
Poincare series
Macdonald identity
correction factor
character expansions
Coxeter groups
JournalPacific Journal of Mathematics
Journal citation313 (1), pp. 159-183
ISSN1945-5844
0030-8730
Year2021
PublisherMSP
Accepted author manuscript
File Access Level
Open (open metadata and files)
Digital Object Identifier (DOI)https://doi.org/10.2140/pjm.2021.313.159
Web address (URL)https://msp.org/pjm/2021/313-1/pjm-v313-n1-p06-p.pdf
Publication dates
Published17 Sep 2021

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