Namikawa has shown that conic symplectic singularities admit a very nice Poisson deformation theory: there exists a universal Poisson deformation over an affine base such that every filtered Poisson deformation can be obtained via base change. A remarkable theorem of Losev shows that filtered quantizations of these varieties are classified by precisely the same data, and he used this to construct a version of the orbit method. For complex simple algebraic group G, he defines a natural embedding from the set of coadjoint orbits of G to the set of completely prime primitive ideals of U(g). Losev conjectured that when G is classical the image of this map should consist of the ideals obtained from one dimensional representations of finite W-algebras via Skryabin’s equivalence. In this talk I will describe my recent proof of this conjecture. One of the main tools is Dirac reduction which allows us to obtain Yangian-type presentations of the semiclassical finite W-algebra, building on the work of Brundan and Kleshchev.

This seminar is a hybrid meeting.
Zoom Meeting ID：832 8055 2567, Passcode : 513212