Morita equivalences between cyclotomic KLR algebras in types ${\mathtt{C}}_{\infty }$ and ${\mathtt{A}}_{\infty }$

Abstract

We prove that level one cyclotomic KLR algebras in type ${\mathtt{C}}_{\infty }$ are graded Morita equivalent to level two cyclotomic KLR algebras in type ${\mathtt{A}}_{\infty }$. We hence deduce the graded decomposition numbers and full submodule structures of all level one cyclotomic KLR algebras in type ${\mathtt{C}}_{\infty }$.

18 pages. v2 has several improvements after comments from a referee

References in corpus (3)

• Graded decomposition numbers for cyclotomic Hecke algebras
• Core blocks for Hecke algebras of type B and sign sequences
• Content systems and deformations of cyclotomic KLR algebras of type $A$ and $C$