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 ${\mathtt{C}}_{\infty }$.

arXiv comment18 pages. v2 has several improvements after comments from a referee

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