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arXiv · 0808.2032

Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

Jonathan Brundan·Alexander Kleshchev
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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.

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BibTeXRIS

Jonathan Brundan, Alexander Kleshchev. 2009-01-28. Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras. https://doi.org/10.1007/s00222-009-0204-8

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