Cellularity and subdivision of KLR and weighted KLRW algebras

Abstract

Weighted KLRW algebras are diagram algebras generalizing KLR algebras. This paper undertakes a systematic study of these algebras culminating in the construction of homogeneous affine cellular bases in affine types A and C, which immediately gives cellular bases for the cyclotomic quotients of these algebras. In addition, we construct subdivision homomorphisms that relate weighted KLRW algebras for different quivers. As an application we obtain new results about the (cyclotomic) KLR algebras of affine type, including (re)proving that the cyclotomic KLR algebras of type A^{(1)}_{e} and C^{(1)}_{e} are graded cellular algebras.

arXiv comment53 pages, revision with several changes, many figures, to appear in Math. Ann., comments welcome

References in corpus (17)

• A diagrammatic approach to categorification of quantum groups I
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• A diagrammatic approach to categorification of quantum groups II
• Graded decomposition numbers for cyclotomic Hecke algebras
• A categorification of quantum sl(2)
• Knot invariants and higher representation theory
• Rouquier's conjecture and diagrammatic algebra
• Affine highest weight categories and affine quasihereditary algebras
• Affine Cellularity of Khovanov-Lauda-Rouquier algebras in type A
• Specht modules for quiver Hecke algebras of type $C$
• ${\mathfrak{gl}}_n$-webs, categorification and Khovanov-Rozansky homologies
• Relative cellular algebras
• Cellularity for weighted KLRW algebras of types $B$, $A^{(2)}$, $D^{(2)}$
• Graded dimensions and monomial bases for the cyclotomic quiver Hecke algebras
• Categorical representations and KLR algebras
• HOMFLYPT homology for links in handlebodies via type A Soergel bimodules
• Weighted Khovanov-Lauda-Rouquier algebras

Cited by in corpus (4)

• Sandwich cellularity and a version of cell theory
• Content systems and deformations of cyclotomic KLR algebras of type $A$ and $C$
• Representation type of higher level cyclotomic quiver Hecke algebras in affine type C
• Cellularity of KLR and weighted KLRW algebras via crystals