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Quiver Schur algebras and q-Fock space
We develop a graded version of the theory of cyclotomic q-Schur algebras, in the spirit of the work of Brundan-Kleshchev on Hecke algebras and of Ariki on q-Schur algebras. As an application, we
Knot Invariants and Higher Representation Theory
We construct knot invariants categorifying the quantum knot variants for all representations of quantum groups. We show that these invariants coincide with previous invariants defined by Khovanov for
Quantizations of conical symplectic resolutions I: local and global structure
We re-examine some topics in representation theory of Lie algebras and Springer theory in a more general context, viewing the universal enveloping algebra as an example of the section ring of a
2-block Springer fibers: convolution algebras and coherent sheaves
For a fixed 2-block Springer fiber, we describe the structure of its irreducible components and their relation to the Bialynicki-Birula paving, following work of Fung. That is, we consider the space
Canonical bases and higher representation theory
  • B. Webster
  • Mathematics
    Compositio Mathematica
  • 1 September 2012
Abstract This paper develops a general theory of canonical bases and how they arise naturally in the context of categorification. As an application, we show that Lusztig’s canonical basis in the
Quantizations of conical symplectic resolutions II: category $\mathcal O$ and symplectic duality
We define and study category $\mathcal O$ for a symplectic resolution, generalizing the classical BGG category $\mathcal O$, which is associated with the Springer resolution. This includes the
Knot invariants and higher representation theory I: diagrammatic and geometric categorification of tensor products
In this paper, we study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. Our aim is to construct knot
A geometric construction of colored HOMFLYPT homology
The aim of this paper is two-fold. First, we give a fully geometric description of the HOMFLYPT homology of Khovanov-Rozansky. Our method is to construct this invariant in terms of the cohomology of
Yangians and quantizations of slices in the affine Grassmannian
We study quantizations of transverse slices to Schubert varieties in the affine Grassmannian. The quantization is constructed using quantum groups called shifted Yangians --- these are subalgebras of
On uniqueness of tensor products of irreducible categorifications
In this paper, we propose an axiomatic definition for a tensor product categorification. A tensor product categorification is an abelian category with a categorical action of a Kac–Moody algebra