Integral Basis Theorem of cyclotomic Khovanov-Lauda-Rouquier algebras of Type A

Abstract

In this paper we prove that the cyclotomic Khovanov-Lauda-Rouquier algebras in type A, ${\mathcal{R}}_n^{\Lambda }$, are $\mathbb{Z}$-free. We then extend the graded cellular basis of ${\mathcal{R}}_n^{\Lambda }$ constructed by Hu and Mathas to ${\mathcal{R}}_n$ and use this basis to give a classification of all irreducible ${\mathcal{R}}_n$-modules.

References in corpus (6)

• A diagrammatic approach to categorification of quantum groups I
• 2-Kac-Moody algebras
• Graded Specht modules
• Knot invariants and higher representation theory I: diagrammatic and geometric categorification of tensor products
• A KLR Grading of the Brauer Algebras
• Graded induction for Specht modules

Cited by in corpus (6)

• The many graded cellular bases of Hecke algebras
• ${\mathfrak{gl}}_n$-webs, categorification and Khovanov-Rozansky homologies
• Seminormal forms and cyclotomic quiver Hecke algebras of type $A$
• p-DG cyclotomic nilHecke algebras
• Content systems and deformations of cyclotomic KLR algebras of type $A$ and $C$
• p-DG cyclotomic nilHecke algebras II