Bowman, C., Hazi, A. orcid.org/0000-0001-7264-2211 and Norton, E. (2022) The modular Weyl–Kac character formula. Mathematische Zeitschrift, 302 (4). pp. 2207-2232. ISSN: 0025-5874
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
| Item Type: | Article |
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| Copyright, Publisher and Additional Information: | © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Hecke categories; p-Kazhdan-Lusztig polynomials; Weyl-Kac character formula |
| Dates: |
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| Institution: | The University of Leeds |
| Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) |
| Date Deposited: | 15 Apr 2026 13:07 |
| Last Modified: | 15 Apr 2026 13:07 |
| Published Version: | https://link.springer.com/article/10.1007/s00209-0... |
| Status: | Published |
| Publisher: | Springer Nature |
| Identification Number: | 10.1007/s00209-022-03084-7 |
| Related URLs: | |
| Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:239914 |

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