Geometry of the Affine Closure of T^*(SL_n/U)
Time: 2021-09-15
Published By: He Liu
Speaker(s): Boming Jia (University of Chicago)
Time: 14:30-15:30 September 16, 2021
Venue: Room 9, Quan Zhai, BICMR
In this talk, I am going to explain geometric properties of the affine closure of the cotangent space of the basic affine space G/U. We will only consider G=SL_n, in which case we can prove that $\overline{T^*(SL_n/U)}$ has symplectic singularity (in the sense of Beauville). A double quiver construction of this affine closure by Dancer, Kirwan, Swann will be explained. In particular, when n=3, we can use this construction to show that this affine closure $\overline{T^*(SL_3/U)}$ is isomorphic to the minimal nilpotent orbit closure in so(8,C) as symplectic varieties. Moreover, the quasi-classical Gelfand-Graev action constructed by Ginzburg and Kazhdan, can be identified with the Triality action on so(8) when restricted to the minimal orbit closure.
