USaskatchewan-PIMS GAP Seminar: Siwei Xu

The main objects of my talk are the affine Yangian and the quantum toroidal algebra of type A with two deformation parameters, as introduced in the work of Bershtein and Tsymbaliuk (2019). These algebras first appeared in Maulik and Okounkov’s 2012 work, where they were realized in a purely geometric form through the equivariant cohomology of quiver varieties. In this talk, I construct an explicit functor from an appropriate category of representations of the affine Yangian associated with $\mathfrak{sl}(mn)$to that of the quantum toroidal algebra associated with $\mathfrak{sl}(mn)$for all positive integers m and n, which extends the construction of Gautam and Toledano Laredo (2016).