Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

Abstract

We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) Khovanov-Lauda algebras in type A. These isomorphisms connect the categorification conjecture of Khovanov and Lauda to Ariki's categorification theorem. The Khovanov-Lauda algebras are naturally graded, which allows us to exhibit a non-trivial Z-grading on blocks of cyclotomic Hecke algebras, including symmetric groups in positive characteristic.

arXiv comment32 pages; minor changes to section 6

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• Categorification of Highest Weight Modules via Khovanov-Lauda-Rouquier Algebras
• Crystals from categorified quantum groups
• Graded Specht modules
• Knot invariants and higher representation theory I: diagrammatic and geometric categorification of tensor products
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• Rouquier's conjecture and diagrammatic algebra
• Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras
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• Graded $q$-Schur algebras
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• Trace as an alternative decategorification functor
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• Affine wreath product algebras
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