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Highest weight categories arising from Khovanov's diagram algebra IV: the general linear supergroup

- J. Brundan, C. Stroppel
- Mathematics
- 15 July 2009

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

- J. Brundan, C. Stroppel
- Mathematics
- 9 June 2008

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… Expand

Gradings on walled Brauer algebras and Khovanov’s arc algebra

- J. Brundan, C. Stroppel
- Mathematics
- 5 July 2011

Quiver Schur algebras and q-Fock space

- C. Stroppel, B. Webster
- Mathematics
- 5 October 2011

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… Expand

2-block Springer fibers: convolution algebras and coherent sheaves

- C. Stroppel, B. Webster
- Mathematics
- 14 February 2008

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… Expand

Highest weight categories arising from Khovanov's diagram algebra II: Koszulity

- J. Brundan, C. Stroppel
- Mathematics
- 20 June 2008

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… Expand

Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors

- C. Stroppel
- Mathematics
- 15 February 2005

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… Expand

Highest weight categories arising from Khovanov's diagram algebra III: category O

- J. Brundan, C. Stroppel
- Mathematics
- 5 December 2008

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… Expand

Quadratic duals, Koszul dual functors, and applications

- V. Mazorchuk, S. Ovsienko, C. Stroppel
- Mathematics
- 20 March 2006

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… Expand

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