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.
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