Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras.

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. [ABSTRACT FROM AUTHOR]