The modular Weyl–Kac character formula

Abstract

We classify and explicitly construct the irreducible graded representations of anti-spherical Hecke categories which are concentrated 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 p-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 fields of arbitrary characteristic.

Metadata

Authors/Creators:

Bowman, Christopher https://orcid.org/0000-0001-6046-8930
Hazi, Amit
Norton, Emily

Funding Information: We would like to thank George Lusztig and Stephen Donkin for their helpful comments. We would also like to thank the anonymous referees for their detailed reading of the paper and their helpful suggestions. The authors are grateful for funding from EPSRC grant EP/V00090X/1, the Royal Commission for the Exhibition of 1851, and European Research Council grant No. 677147, respectively. Publisher Copyright: © 2022, The Author(s).

Keywords:

Hecke categories, p-Kazhdan-Lusztig polynomials, Weyl-Kac character formula

Dates: