Shilin Yu: Duality of nilpotent orbit covers

Speaker:  Shilin Yu, Xiamen University

In their study of special unipotent representations for complex semisimple groups, Lusztig-Spaltenstein and Barbasch-Vogan defined a duality map between the nilpotent orbits of G and that of its Langlands dual group G^∨, which is related to the special unipotent representations of G.  This duality was later generalized by Sommers, Achar and Losev-Mason-Brown-Matvieievskyi in various forms.

In this talk, I will reinterpret these duality maps in terms of covers of nilpotent orbits. This not only enables the definition of generalized unipotent representations, but also leads to interesting observations and conjectures regarding the birational geometry of the affinizations of the nilpotent orbit covers. If time permits, I will also discuss the connection of these findings to symplectic duality/3d mirror symmetry. 

The talk is partially based on joint work with Lucas Mason-Brown and Dmytro Matvieievskyi (arXiv:2309.14853) and ongoing project with Daniel Juteau, Paul Levy, and Eric Sommers.