Affine Yangians and quantum toroidal algebras in type A

Abstract: 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 $\mathfrak{sl}(m)$ for all positive integers m and n, which extends the construction of Gautam and Toledano Laredo (2016).

mathematical physicsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Comments: Hybrid delivery (in person on University of Saskatchewan campus and via Zoom).

PIMS Geometry / Algebra / Physics (GAP) Seminar