Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
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- Brundan, J. & Kleshchev, A. Invent. math. (2009) 178: 451. doi:10.1007/s00222-009-0204-8
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We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) cyclotomic 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.