论文标题
量子仿射对称对和Erientifold KLR代数
Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras
论文作者
论文摘要
令$ \ mathfrak {g} $为一个复杂的简单谎言代数和$ u_ql \ mathfrak {g} $相应的量子仿射代数。 We construct a functor ${}^θ{\sf F}$ between finite-dimensional modules over a quantum symmetric pair of affine type $U_q\mathfrak{k}\subset U_qL{\mathfrak{g}}$ and an orientifold KLR algebra arising from a framed quiver with a contravariant involution, providing a boundary analogue Kang-kashiwara-kim-oh广义的schur-weyl二元性。关于它们的结构，我们的组合模型进一步丰富了三角k-matrix的杆子，使$ u_q \ mathfrak {k} $在有限二维$ u_ql {\ mathfrak {\ mathfrak {g}}} $ - modules上的动作交织在一起。通过构造，$ {}^θ{\ sf f} $自然与kang-kashiwara-kim-oh函子兼容，而后者是单型类别的函数，$ {}^θ{}^θ{\ sf f} $是模块类别的函数。依靠合适的同构 - la brundan-kleshchev-rouquier，我们证明$ {}^θ{\ sf f} $恢复了由于fan-split类型$ \ sf aiii $ $ \ sf aiii $的fan lai-li-luo-wang-watanabe而导致的schur-weyl二元性。
Let $\mathfrak{g}$ be a complex simple Lie algebra and $U_qL\mathfrak{g}$ the corresponding quantum affine algebra. We construct a functor ${}^θ{\sf F}$ between finite-dimensional modules over a quantum symmetric pair of affine type $U_q\mathfrak{k}\subset U_qL{\mathfrak{g}}$ and an orientifold KLR algebra arising from a framed quiver with a contravariant involution, providing a boundary analogue of 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 $U_q\mathfrak{k}$ on finite-dimensional $U_qL{\mathfrak{g}}$-modules. By construction, ${}^θ{\sf F}$ is naturally compatible with the Kang-Kashiwara-Kim-Oh functor in that, while the latter is a functor of monoidal categories, ${}^θ{\sf F}$ is a functor of module categories. Relying on a suitable isomorphism à la Brundan-Kleshchev-Rouquier, we prove that ${}^θ{\sf F}$ recovers the Schur-Weyl dualities due to Fan-Lai-Li-Luo-Wang-Watanabe in quasi-split type $\sf AIII$.
