Coordinate ring of the universal centralizer via Demazure operators (Tom Gannon, UCR)

One of the key objects used in Ngo’s proof of the fundamental lemma is the group scheme of universal centralizers associated to a split reductive group G. In this talk, we’ll discuss forthcoming work, joint with Victor Ginzburg, which describes the coordinate ring of the group scheme of universal centralizers in terms of the root datum of G using Demazure (or divided difference) operators. We will then discuss how our result follows from a more general computation on Weil restriction and, time permitting, we will discuss a potential generalization of our result to Coulomb branches.