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

By Jonathan Brundan, C. Stroppel. 2008

149 citations recorded by the source corpus.

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 “projective functors” in our setting. As an application, we give a direct proof of the fact that the quasi-hereditary covers of generalised Khovanov algebras are Koszul.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/15062d1344d18557b707f004783f8c2ad087decb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Cohomology of generalized supergrassmannians and character formulae for basic classical Lie superalgebras (2009, unknown): “Brundan’s method was developed further in [8], [4], [5], [6], [7].”
Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, background): “More generally, for link homology theories associated with fundamental sln representations, Webster describes an isomorphism relating his construction to Sussan’s category O based link homology theory [69] , which is related via Koszul duality to a theory defined by Mazorchuk and Stroppel [56].”
Categorifying fractional Euler characteristics, Jones–Wenzl projectors and 3j-symbols (2012, methodology): “The simple modules with minimal Gelfand–Kirillov dimension correspond under Koszul duality to precisely the projective modules which are also tilting; see [11], Theorem 6.”
2-block Springer fibers: convolution algebras and coherent sheaves (2008, methodology): “Based on the results of this paper, the slight generalization from components to arbitrary stable manifolds should not be too difficult by mimicking [BS10], Section 6.”
Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A (2009, methodology): “Just as with the original denition of cellular algebras, graded cellular algebras are already implicit in the literature in the work of Brundan and Stroppel [ 9 , 10].”