Highest Weight Categories Arising from Khovanov's Diagram Algebra I: Cellularity

By Jonathan Brundan, C. Stroppel. 2008

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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 certain infinite dimensional limiting versions K m , K m and K ∞ . In this article we prove that H n m is a cellular symmetric algebra and that Kn m is a cellular quasi-hereditary algebra. In subsequent articles, we relate Hn m , Kn m and K m to level two blocks of degenerate cyclotomic Hecke algebras, parabolic category O and the general linear supergroup, respectively.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/96eb0dc2bd1c672ace41ed88c497027051c147b9

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Citations in the corpus

Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality (2013, unknown): “ˇ +BˇEˇ2 1 = 0, Fˇ2 1 Bˇ −(q +q−1)Fˇ BˇFˇ +BˇFˇ2 1 = 0, Bˇ2Eˇ 1 −(q +q−1)BˇEˇ1Bˇ +Eˇ1Bˇ2 = Eˇ1, Bˇ2Fˇ 1 −(q +q−1)BˇFˇ1Bˇ +Fˇ1Bˇ2 = Fˇ1. 44 MICHAEL EHRIG AND CATHARINA STROPPEL 6.3. Action on ⋀n V. In [BS11a], a calculus of diagrammatic weights and diagrammatic algebras was introduced to describe max”
Annular Khovanov homology and knotted Schur–Weyl representations (2015, background): “1The construction of this functor-valued tangle invariant is made more explicit in [11] than in [8], whose focus is on a relationship between the algebras An and category O.”
Categorifying fractional Euler characteristics, Jones–Wenzl projectors and 3j-symbols (2012, background): “In these cases the Koszul dual algebra A k;n can be defined diagrammatically (see [10] and [12]) by slightly generalizing Khovanov’s arc algebra from [35].”
Cohomology of generalized supergrassmannians and character formulae for basic classical Lie superalgebras (2009, unknown): “Brundan’s method was developed further in [7], [4], [5] and [6].”
Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A (2009, background): “R T ] 1 5 Fe b This paper constructs an explicit homogeneous cellular basis for the cyclotomic Khovanov– Lauda–Rouquier algebras of type A. Keywords: Cyclotomic Hecke algebras, Khovanov–Lauda–Rouquier algebras, cellular algebras 2000 MSC: 20C08, 20C30”
Quantum link homology via trace functor I (2016, methodology): “It was proven by Brundan and Stroppel that arc algebras have finite global dimension [BS11].”
Quiver Hecke Algebras and 2-Lie Algebras (2011, methodology): “We discuss quiver Hecke algebras [28], which have been introduced independently by Khovanov and Lauda [15, 17], and their cyclotomic versions, which have been considered independently in the case of level 2 weights for type A, by Brundan and Stroppel [5].”