Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

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

References in corpus (3)

• 2-Kac-Moody algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Blocks of cyclotomic Hecke algebras

Cited by in corpus (9)

• 2-Kac-Moody algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Categorifications from planar diagrammatics
• Graded induction for Specht modules
• Representations of Khovanov-Lauda-Rouquier Algebras and Combinatorics of Lyndon Words
• Derived equivalences and sl_2-categorifications for U_q(gl_n)
• An interpretation of the Lascoux-Leclerc-Thibon algorithm and graded representation theory
• Representation Theory of Symmetric Groups and Related Hecke Algebras
• sl_2-actions along short strings for spin blocks