Inventiones mathematicae

, 178:451

Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

Article

DOI: 10.1007/s00222-009-0204-8

Cite this article as:
Brundan, J. & Kleshchev, A. Invent. math. (2009) 178: 451. doi:10.1007/s00222-009-0204-8

Abstract

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.

Mathematics Subject Classification (2000)

20C08

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OregonEugeneUSA