Algebra Seminar: Yacobi -- On the category O of affine Grassmannian slices

Oded Yacobi (The University of Sydney) 

Friday 11 May, 12-1pm, Place: Carslaw 375 

Title: On the category O of affine Grassmannian slices 

Abstract: Affine grassmannian slices are varieties which appear naturally in geometric
representation theory.  Their quantisations are given by truncated shifted Yangians.  I
will describe a recent result which gives an equivalence of categories between modules
for truncated shifted Yangians and modules for Khovanov-Lauda-Rouquier-Webster
algebras.  We use this theorem to a) resolve a conjecture describing the highest weights
of truncated shifted Yangians, and b) prove the so-called "symplectic duality" between
affine Grassmannian slices and Nakajima quiver varieties.  The latter result provides a
link between two very different geometric models for representations of semisimple Lie
algebras.  This is joint work with Kamnitzer, Tingley, Webster, and Weekes.