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Twisting functors on
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, weExpand
Highest weight categories arising from Khovanov's diagram algebra IV: the general linear supergroup
We prove that blocks of the general linear supergroup are Morita equivalent to a limiting version of Khovanov's diagram algebra. We deduce that blocks of the general linear supergroup are Koszul.
Highest Weight Categories Arising from Khovanov's Diagram Algebra I: Cellularity
This is the first of four articles studying some slight generalisations Hn m of Khovanov’s diagram algebra, as well as quasi-hereditary covers Kn m of these algebras in the sense of Rouquier, andExpand
Gradings on walled Brauer algebras and Khovanov’s arc algebra
Abstract We introduce some Z -graded versions of the walled Brauer algebra B r , s ( δ ) , working over a field of characteristic zero. This allows us to prove that B r , s ( δ ) is Morita equivalentExpand
Highest weight categories arising from Khovanov's diagram algebra III: category O
We prove that integral blocks of parabolic category O associated to the subalgebra gl(m) x gl(n) of gl(m+n) are Morita equivalent to quasi-hereditary covers of generalised Khovanov algebras. AlthoughExpand
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 spaceExpand
Highest weight categories arising from Khovanov's diagram algebra II: Koszulity
This is the second of a series of four papers studying various generalisations of Khovanov's diagram algebra. In this paper we develop the general theory of Khovanov's diagrammatically definedExpand
Quadratic duals, Koszul dual functors, and applications
This paper studies quadratic and Koszul duality for modules over positively graded categories. Typical examples are modules over a path algebra, which is graded by the path length, of a notExpand
Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors
To each generic tangle projection from the three-dimensional real vector space onto the plane, we associate a derived endofunctor on a graded parabolic version of the Bernstein-Gel'fand categoryExpand
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