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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.
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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, and…
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Twisting functors on
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Gradings on walled Brauer algebras and Khovanov’s arc algebra
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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…
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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…
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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 defined…
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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 category…
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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. Although…
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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 not…
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