Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

Understand

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.