Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
arXiv:0808.2032 · doi:10.1007/s00222-009-0204-8
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.
32 pages; minor changes to section 6