Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

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.Comment: 32 pages; minor changes to section

Completely splittable representations of affine Hecke-Clifford algebras

We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to 2.Comment: 39 pages, v2, added a new reference with comments in section 4.4, added two examples (Example 5.4 and Example 5.11) in section 5, mild corrections of some typos, to appear in J. Algebraic Combinatoric

The degenerate analogue of Ariki's categorification theorem

We explain how to deduce the degenerate analogue of Ariki's categorification theorem over the ground field C as an application of Schur-Weyl duality for higher levels and the Kazhdan-Lusztig conjecture in finite type A. We also discuss some supplementary topics, including Young modules, tensoring with sign, tilting modules and Ringel duality.Comment: 44 page

On representation theory of affine Hecke algebras of type B

Ariki's and Grojnowski's approach to the representation theory of affine Hecke algebras of type $A$ is applied to type $B$ with unequal parameters to obtain -- under certain restrictions on the eigenvalues of the lattice operators -- analogous multiplicity-one results and a classification of irreducibles with partial branching rules as in type $A$.Comment: to appear in Algebras and Representation theor