Affine Grassmannian slices are symplectic singularities that appear throughout representation theory and physics—for instance as Coulomb branches of quiver gauge theories, in geometric Satake, and in the (quantum) Mirković–Vybornov isomorphism. A theorem of Kamnitzer–Webster–Weekes–Yacobi shows that these slices are quantised by truncated shifted Yangians.
In 2023, Lu–Wang–Zhang gave a Drinfeld presentation of the twisted Yangian of type AI, making it possible to define shifted twisted Yangians. In this talk I will describe joint work with R. Bartlett and T. Przezdziecki extending the Kamnitzer–Webster–Weekes–Yacobi picture to the twisted setting. We show that truncated shifted twisted Yangians quantise symmetric quotients of slices or equivalently fixed-point loci of slices under involutions.
I will begin by explaining the untwisted KWWY story with minimal prerequisites, and then turn to the twisted type AI case and the new features that arise.