University of Sydney Algebra Seminar

Oded Yacobi (University of Sydney)

Friday 19th July, 12:05-12:55pm, Carslaw 373

Yangians and slices in the affine Grassmannian

I will discuss an ongoing project with Kamnitzer, Webster, and Weekes to study quantizations of slices in the affine Grassmannian. These slices arise as symplectic leaves of the affine Grassmannian and are also natural from the point of view of geometric representation theory. We describe a quantization of these slices constructed from certain quantum groups called Yangians. Currently we are studying categories of modules over these quantizations, with the goal of proving that these categories are endowed with certain Lie algebra actions in the sense of Khovanov-Lauda and Rouquier. This talk will be introductory; no prior knowledge of these ideas will be assumed.