Cellularity of KLR and weighted KLRW algebras via crystals

Abstract

We prove that the weighted KLRW algebras of finite type, and their cyclotomic quotients, are cellular algebras. The cellular bases are explicitly described using crystal graphs. As a special case, this proves that the KLR algebras of finite type are cellular. As one application, we give explicit formulas for the graded decomposition numbers of the cyclotomic algebras in level one.

57 pages, many figures. Updated final version for publication

References in corpus (8)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Blocks of cyclotomic Hecke algebras
• Affine highest weight categories and affine quasihereditary algebras
• Graded dimensions and monomial bases for the cyclotomic quiver Hecke algebras
• Cellularity for weighted KLRW algebras of types $B$, $A^{(2)}$, $D^{(2)}$
• Cellularity and subdivision of KLR and weighted KLRW algebras
• Sandwich cellularity and a version of cell theory