A brief review of abelian categorifications.
A combinatorial formula for orthogonal idempotents in the 0-Hecke algebra of the symmetric group.
Affine Hecke algebras and orthogonal polynomials
An expansion of the Jones representation of genus 2 and the Torelli group.
Cells and constructible representations in type .
Character polynomials, their -analogs and the Kronecker product.
Constant term identities, orthogonal polynomials and affine Hecke algebras.
Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras
We define the -restriction and -induction functors on the category of the cyclotomic rational double affine Hecke algebras. This yields a crystal on the set of isomorphism classes of simple modules, which is isomorphic to the crystal of a Fock space.
Decomposition numbers of finite classical groups for linear primes.
Diagram algebras, Hecke algebras and decomposition numbers at roots of unity
From double Hecke algebra to analysis.
Fully commutative Kazhdan-Lusztig cells
We investigate the compatibility of the set of fully commutative elements of a Coxeter group with the various types of Kazhdan-Lusztig cells using a canonical basis for a generalized version of the Temperley-Lieb algebra.
Generalized Induction of Kazhdan-Lusztig cells
Following Lusztig, we consider a Coxeter group together with a weight function. Geck showed that the Kazhdan-Lusztig cells of are compatible with parabolic subgroups. In this paper, we generalize this argument to some subsets of which may not be parabolic subgroups. We obtain two applications: we show that under specific technical conditions on the parameters, the cells of certain parabolic subgroups of are cells in the whole group, and we decompose the affine Weyl group of type into left...
Grothendieck bialgebras, partition lattices, and symmetric functions in noncommutative variables.
Group rings, Hecke orders, quasi-hereditary orders, cellular orders and deformations.
Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products
The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras...
Hecke-Clifford algebras and spin Hecke algebras. IV: Odd double affine type.
Higher dimensional algebra. VII: Groupoidification.
Homfly polynomials of generalized Hopf links.
Homogeneous representations of Khovanov–Lauda Algebras
We construct irreducible graded representations of simply laced Khovanov–Lauda algebras which are concentrated in one degree. The underlying combinatorics of skew shapes and standard tableaux corresponding to arbitrary simply laced types has been developed previously by Peterson, Proctor and Stembridge. In particular, the Peterson–Proctor hook formula gives the dimensions of the homogeneous irreducible modules corresponding to straight shapes.