# Oded Yacobi (University of Sydney)

## Highest weight theory for truncated shifted Yangians

Truncated shifted Yangians are a family of noncommutative algebras associated to a semisimple Lie algebra $$\mathfrak{g}$$, which in type $$A$$ are known to quantise slices to spherical Schubert varieties in the affine Grassmannian (in general type it still a conjecture). In this talk we'll motivate the construction of these algebras and then discuss how to control their highest weights using (somewhat mysterious) finite dimensional representations of $$\mathfrak{g}$$.