The modular Weyl-Kac character formula
Representation Theory
2023-01-20 v4 Combinatorics
Abstract
We classify and explicitly construct the irreducible graded representations of anti-spherical Hecke categories which are concentrated in one degree. Each of these homogeneous representations is one-dimensional and can be cohomologically constructed via a BGG resolution involving every (infinite dimensional) standard representation of the category. We hence determine the complete first row of the inverse parabolic -Kazhdan--Lusztig matrix for an arbitrary Coxeter group and an arbitrary parabolic subgroup. This generalises the Weyl--Kac character formula to all Coxeter systems (and their parabolics) and proves that this generalised formula is rigid with respect to base change to an arbitrary field.
Cite
@article{arxiv.2004.13082,
title = {The modular Weyl-Kac character formula},
author = {Chris Bowman and Amit Hazi and Emily Norton},
journal= {arXiv preprint arXiv:2004.13082},
year = {2023}
}