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

References in corpus (19)

• A diagrammatic approach to categorification of quantum groups I
• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Blocks of cyclotomic Hecke algebras
• Graded Specht modules
• Affine sl_p controls the representation theory of the symmetric group and related Hecke algebras
• Rouquier's conjecture and diagrammatic algebra
• Universal Specht modules for cyclotomic Hecke algebras
• Schur elements for the Ariki-Koike algebra and applications
• Modular representation theory in type A via Soergel bimodules
• Affine Cellularity of Khovanov-Lauda-Rouquier algebras in type A
• Proof of Varagnolo-Vasserot conjecture on cyclotomic categories O
• Cellules de Calogero-Moser
• Generalised column removal for graded homomorphisms between Specht modules
• Characteristic-free bases and BGG resolutions of unitary simple modules for quiver Hecke and Cherednik algebras
• Integral Basis Theorem of cyclotomic Khovanov-Lauda-Rouquier algebras of Type A
• Graded cellular basis and Jucys-Murphy elements for generalized blob algebras
• Modular decomposition numbers of cyclotomic Hecke and diagrammatic Cherednik algebras: A path theoretic approach

Cited by in corpus (7)

• Characteristic-free bases and BGG resolutions of unitary simple modules for quiver Hecke and Cherednik algebras
• Blob algebra approach to modular representation theory
• Graded cellular basis and Jucys-Murphy elements for generalized blob algebras
• Blob algebra and two-color Soergel calculus
• The nil-blob algebra: An incarnation of type ${\tilde{A}}_1$ Soergel calculus and of the truncated blob algebra
• Modular decomposition numbers of cyclotomic Hecke and diagrammatic Cherednik algebras: A path theoretic approach
• Path combinatorics and light leaves for quiver Hecke algebras