The many graded cellular bases of Hecke algebras

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.

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