The many graded cellular bases of Hecke algebras
Representation Theory
2026-02-18 v9
Abstract
We settle a long-standing problem in the theory of Hecke algebras of complex reflection groups by constructing many (graded) integral cellular bases of these algebras. As applications, we explicitly construct the simple modules of Ariki's categorification theorem and prove unitriangularity of decomposition matrices over arbitrary fields, we also prove Martin-Woodcock's conjecture.
Keywords
Cite
@article{arxiv.1702.06579,
title = {The many graded cellular bases of Hecke algebras},
author = {C. Bowman},
journal= {arXiv preprint arXiv:1702.06579},
year = {2026}
}
Comments
The combinatorics has been changed to make it more accessible to those with a background in Fock spaces. Includes a new ordering on diagrams which vastly simplifies a number of proofs