Jonathan Brundan

Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

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.

Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra (|)

The problem of computing the characters of the finite dimensional irreducible representations of the Lie superalgebra

Graded decomposition numbers for cyclotomic Hecke algebras

\mathfrak{gl}(m|n)

Highest weight categories arising from Khovanov's diagram algebra II: Koszulity

over

HIGHEST WEIGHT CATEGORIES ARISING FROM KHOVANOV'S DIAGRAM ALGEBRA IV: THE GENERAL LINEAR SUPERGROUP

\C

Graded Specht modules

was solved a few years ago by V. Serganova. In this article, we present an entirely different approach. One consequence is a direct and elementary proof of a conjecture made by van der Jeugt and Zhang for the composition multiplicities of Kac modules. This does not seem to follow easily from Serganovas formula, since that involves certain alternating sums. We also compute Exts between simple modules in the category of finite dimensional representations, and formulate for the first time a conjecture for the characters of the infinite dimensional irreducible representations in the analogue of category

A New Proof of the Mullineux Conjecture

\mathcal O

Representations of shifted Yangians and finite -algebras

for the Lie superalgebra

Centers of degenerate cyclotomic Hecke algebras and parabolic category

\mathfrak{gl}(m|n)

Modular Branching Rules and the Mullineux Map for Hecke Algebras of Type A

.