Character expansion of Kac-Moody correction factors
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2019
- DOI:
- 10.48550/arXiv.1911.09770
- arXiv:
- arXiv:1911.09770
- Bibcode:
- 2019arXiv191109770L
- Keywords:
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- Mathematics - Representation Theory;
- 17B22
- E-Print:
- 20 pages, 4 tables