Derived equivalences for cotangent bundles of Grassmannians via categorical 𝔰𝔩2 actions

By Sabin Cautis, Joel Kamnitzer, Anthony M. Licata. 2009

56 citations recorded by the source corpus.

Abstract We construct an equivalence of categories from a strong categorical sl(2) action, following the work of Chuang–Rouquier. As an application, we give an explicit, natural equivalence between the derived categories of coherent sheaves on cotangent bundles to complementary Grassmannians.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/819360b5e8d86a760d7c234322a98ebc963edbd3

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Citations in the corpus

The $\mathfrak{sl}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality (2014, methodology): “Our main tool is the higher representation theory of the Khovanov-Lauda categorified quantum group [25, 26, 27] (see also work of Rouquier [48] for an independent construction), in particular, the categorical skew Howe duality of Cautis-Kamnitzer-Licata [8].”
Implicit structure in 2-representations of quantum groups (2011, background): “annians. In [7] the idea of a “geometric categorical sl2 action” was introduced. In [8] we showed that such an action induces a strong 2-representation of sl2, like the one in section 1.2. In [7] and [6] a geometric categorical sl2 action was constructed on derived categories of coherent sheaves on ”
An introduction to diagrammatic algebra and categorified quantum sl(2) (2011, methodology): “ionof the reﬂection element in the quantum setting wasstudied by Cautis, Kamnitzer, and Licata. They deﬁned an analog of the derived equivalence introduced by Chuang and Rouquier in the context of U˙ [CKL09]. In their setting it suﬃces for the weight categories Vn to be triangulated rather than abel”
Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, methodology): “resulting equivalences are highly nontrivial and have been applied to a variety of contexts ranging from the representation theory of the symmetric group [20] to coherent sheaves on cotangent bundles [16, 14]. Cautis and Kamnitzer later showed that given an integrable 2-representation UQ(slm) → K th”
Braiding via geometric Lie algebra actions (2010, methodology): “] −−→ FIεI (hλ,αii+ s−1) i ∗E (s−1) i [−s+1] ∼= T −1 i (λ). 10 SABIN CAUTIS AND JOEL KAMNITZER Note that T s i (λ) = 0 for s ≫ 0 since we only deal with integrable representations. The main result of [CKL3] is the following. Theorem 2.9. ··· → T s i (λ) ds −→ Ti s−1 i (λ) ds−1 −−−→i ... d1 −→ Ti 0 i”
A diagrammatic categorification of the q-Schur algebra (2010, background): “Cautis, Kamnitzer and Licata [3] also studied the Chuang-Rouquier complex from a geometric point of view.”