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Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

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arxiv 0808.2032 v4 pith:5U25RPXX submitted 2008-08-14 math.RT math.QA

Jonathan Brundan , Alexander Kleshchev This is my paper · ORCID
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keywords algebrasblockscyclotomicheckekhovanov-laudacategorificationallowsariki
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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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