Morita equivalences between cyclotomic KLR algebras in types $\mathtt{C}_\infty$ and $\mathtt{A}_\infty$
Chris Bowman, Robert Muth, Liron Speyer, Louise Sutton
TL;DR
This paper establishes a graded Morita equivalence between certain cyclotomic KLR algebras of types C_infinity and A_infinity, enabling detailed understanding of their module structures and decomposition numbers.
Contribution
It proves a Morita equivalence between level one type C_infinity and level two type A_infinity cyclotomic KLR algebras, revealing their structural similarities.
Findings
Graded Morita equivalence between specified KLR algebras
Determination of graded decomposition numbers
Full submodule structures of level one cyclotomic KLR algebras
Abstract
We prove that level one cyclotomic KLR algebras in type are graded Morita equivalent to level two cyclotomic KLR algebras in type . We hence deduce the graded decomposition numbers and full submodule structures of all level one cyclotomic KLR algebras in type .
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Taxonomy
TopicsAdvanced Operator Algebra Research · Algebraic structures and combinatorial models · Advanced Algebra and Logic