Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras
Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras
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DOI：
10.1016/j.aim.2023.109383
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发表时间：
2022-04
影响因子：
1.7
通讯作者：
Andrea Appel;T. Przeździecki
中科院分区：
文献类型：
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作者：
Andrea Appel;T. Przeździecki
令 g 为复简单李代数，U q L g 为相应的量子仿射代数。我们在仿射型 U q k⊂ U q L g 的量子对称对子代数和由具有逆变对合的框架颤动产生的东方 KLR 代数上的有限维模之间构造函子 F θ ，提供 Kang-Kashiwara-Kim-Oh 广义 Schur-Weyl 对偶性的边界模拟。就其构造而言，我们的组合模型进一步丰富了三角 K 矩阵的极点，该矩阵将 U q k 对有限维 U q L g 模块的作用交织在一起。通过构造，F θ 与 Kang-Kashiwara-Kim-Oh 函子自然兼容，因为后者是幺半群范畴的函子，而 F θ 是模范畴的函子。依靠合适的 Brundan-Kleshchev-Rouquier 同构，我们证明 F θ 恢复了准分裂 AIII 型中由 Fan-Lai-Li-Luo-Wang-Watanabe 引起的 Schur-Weyl 对偶性。
Let g be a complex simple Lie algebra and U q L g the corresponding quantum affine algebra. We construct a functor F θ between finite-dimensional modules over a quantum symmetric pair subalgebra of affine type U q k⊂ U q L g and an orientifold KLR algebra arising from a framed quiver with a contravariant involution, providing a boundary analogue of the Kang-Kashiwara-Kim-Oh generalized Schur-Weyl duality. With respect to their construction, our combinatorial model is further enriched with the poles of a trigonometric K-matrix intertwining the action of U q k on finite-dimensional U q L g-modules. By construction, F θ is naturally compatible with the Kang-Kashiwara-Kim-Oh functor in that, while the latter is a functor of monoidal categories, F θ is a functor of module categories. Relying on a suitable isomorphism à la Brundan-Kleshchev-Rouquier, we prove that F θ recovers the Schur-Weyl dualities due to Fan-Lai-Li-Luo-Wang-Watanabe in quasi-split type AIII.