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

By Jonathan Brundan, C. Stroppel. 2009

199 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1f5c31397cba0e137105e9263ed5a83b3bce47d4

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In Algebra and Number Theory

1. Jonathan Brundan
2. Weiqiang Wang
3. Ben Webster
4. I. Losev
5. Shun-Jen Cheng
6. Ngau Lam
7. Antonio Sartori
8. C. Stroppel

In Geometry and Topology

1. Jonathan Brundan
2. Weiqiang Wang
3. I. Losev
4. Ben Webster
5. C. Stroppel
6. Shun-Jen Cheng
7. Ngau Lam
8. Antonio Sartori

In Mathematical Physics

1. I. Losev
2. Ben Webster
3. Weiqiang Wang
4. Jonathan Brundan
5. Shun-Jen Cheng
6. Ngau Lam
7. Antonio Sartori
8. Aaron D. Lauda

Citations in the corpus

• The brundan-kazhdan-lusztig conjecture for general linear lie superalgebras (2012, background): “n the results of [Br1] a priori, and hence the parabolic versions of the BKL conjecture as formulated in [CW1] followed. There is yet another independent and complete solution by Brundan and Stroppel [BS] toward the irreducible and tilting character problem for the maximal parabolic category Fm|n. A”
• The Alexander polynomial as quantum invariant of links (2013, background): “Namely, it follows from the fact that the category of finite-dimensional Uq(gl(1|1))-modules is not semisimple (this is true even in the non-quantized case and well-known, see for example [4] where the blocks of the category of finite-dimensional gl(m|n)-representations are studied in detail) that t”
• Tensor product categorifications and the super Kazhdan-Lusztig conjecture (2013, background): “or all of the parabolic analogs of O, so that a very special case recovers the Koszul grading on the subcategory of Oconsisting of finite dimensional representations that was constructed explicitly in [BS]. Our main result here can be paraphrased as follows. Theorem A. Any block of parabolic category”
• Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality (2013, unknown): “Theorem D gives a new instance of based categorifications in the context of category O, but now connecting canonical bases of Hecke algebras with canonical bases of quantum symmetric pairs instead of quantum groups as for instance in [BS10], [FKS06], [Sar13], [Web10], see [Maz12] for an overview.”