量子对称对的分类1

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology Pub Date : 2016-05-12 DOI:10.4171/QT/117

Huanchen Bao, P. Shan, Weiqiang Wang, Ben Webster

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引用次数: 25

摘要

通过引入一个$2$-范畴，对量子群$\mathfrak{sl}_{2r+1}$的共理想子代数进行了分类，并证明了自对偶不可分解的$1$-态射对该代数的正则基进行了分类。这使得我们可以定义这个共理想代数在部分标志变异的上同环上的模的范畴和B/C类型的BGG范畴$\mathcal{O}$上的范畴上的范畴作用。

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Categorification of quantum symmetric pairs I

We categorify a coideal subalgebra of the quantum group of $\mathfrak{sl}_{2r+1}$ by introducing a $2$-category a la Khovanov-Lauda-Rouquier, and show that self-dual indecomposable $1$-morphisms categorify the canonical basis of this algebra. This allows us to define a categorical action of this coideal algebra on the categories of modules over cohomology rings of partial flag varieties and on the BGG category $\mathcal{O}$ of type B/C.

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来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.