Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

Details Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

2008-08-14

arxiv.org/abs/0808.2032v4

Invent. Math. 178 (2009), 451-484.

Mathematics

Representation Theory

32 pages; minor changes to section 6

Scientific paper

10.1007/s00222-009-0204-8

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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