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

by Andrea Appel (Università di Parma, Italy)

Thursday 2 Dec 2021, 15:00 → 16:00 Europe/Rome

Aula Magna (Dipartimento di Matematica)

​In the work of Kang, Kashiwara, and Kim, the Schur–Weyl duality between quantum affine algebras and affine Hecke algebras is extended to certain Khovanov-Lauda-Rouquier (KLR) algebras, whose defining combinatorial datum is given by the poles of the normalized $R$–matrix on a set of representations.
In this talk, I will describe a boundary version of this construction, providing a Schur–Weyl duality between quantum symmetric pairs of affine type and KLR algebras arising from a framed quiver with an involution. With respect to the Kang-Kashiwara-Kim construction, the extra combinatorial datum we take into account is given by the poles of the $k$–matrix (that is, a solution of the reflection equation) of the quantum symmetric pair. This is based on joint work in progress with T. Przezdziecki.