Cellularity of KLR and wKLRW algebras via crystals

Communications of the American Mathematical Society 2026 Open access

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Authors: Andrew Mathas, Daniel Tubbenhauer
DOI: 10.1090/cams/61
Cited by: 0
References: 49

Abstract

We prove that the weighted Khovanov–Lauda–Rouquier–Webster algebras of finite type, and their cyclotomic quotients, are sandwich cellular algebras. The sandwich cellular bases are explicitly described using crystal graphs. As a special case, this proves that the Khovanov–Lauda–Rouquier algebras of finite type are sandwich cellular. As one of our applications, we give explicit formulas for some graded decomposition numbers of the cyclotomic algebras in level one.

Fields of Study & Subjects

Geometric and Algebraic Topology Rings Modules and Algebras Finite Group Theory Research

Publication details

Journal / source
Communications of the American Mathematical Society
Volume
6
Issue
11
Pages
548–633
Publication date
13 May 2026
Language
EN