The many graded cellular bases of Hecke algebras

2017/02/21 by C. Bowman, Bowman, C. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1702.06579

openalex publication_date 2017/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Cellules de Calogero-Moser
• Integral Basis Theorem of cyclotomic Khovanov-Lauda-Rouquier algebras of Type A
• 2-Kac-Moody algebras
• Graded cellular bases for Temperley–Lieb algebras of type A and B
• Characteristic-free bases and BGG resolutions of unitary simple modules for quiver Hecke and Cherednik algebras
• Graded cellular basis and Jucys-Murphy elements for generalized blob\n algebras
• Proof of Varagnolo-Vasserot conjecture on cyclotomic categories O

Cited by

• A Specht Filtration of Permutation Modules Over KLR Algebras

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