Highest weight categories arising from Khovanov's diagram algebra III: category O
By Jonathan Brundan, C. Stroppel. 2008
218 citations recorded by the source corpus.
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 this result is in principle known, the existing proof is quite indirect, going via perverse sheaves on Grassmannians. Our new approach is completely algebraic, exploiting Schur-Weyl duality for higher levels. As a by-product we get a concrete combinatorial construction of 2-Kac-Moody representations in the sense of Rouquier corresponding to level two weights in finite type A.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/36ae5708223acefc9039b6e163c9510132d12cb8
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In Geometry and Topology
- Aaron D. Lauda
- C. Stroppel
- Mikhail Khovanov
- Joshua Sussan
- I. Frenkel
- Ben Webster
- David E. V. Rose
- Jonathan Brundan
In Mathematical Physics
- Aaron D. Lauda
- C. Stroppel
- Joshua Sussan
- I. Frenkel
- Mikhail Khovanov
- Ben Webster
- David E. V. Rose
- Vera Serganova
Citations in the corpus
- Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality (2013, unknown): “This property plays an important role in the context of categorification of modules over quantum groups, [70], [17], [20].”
- 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].”
- Crystals from categorified quantum groups (2009, background): “A special case of this conjecture was proven in type A by Brundan and Stroppel [12].”
- Cohomology of generalized supergrassmannians and character formulae for basic classical Lie superalgebras (2009, methodology): “solved this problem by a different, purely algebraic, method and discovered a remarkable connection with the representation theory of gl(∞). Brundan’s method was developed further in [7], [4], [5] and [6]. Inthispaperwegeneralise the methodof [23]to the orthosymplectic groupsOSP(m,2n). The results we”