Seminar

Representation theory seminar 2024 Semester 2

Organisers: Dougal DavisKari Vilonen, Ting Xue

Place and time: Peter Hall 162, 2:15-4:15PM

Please contact one of the organisers to be added to the mailing list.

Upcoming Seminars

 

Aug 1: Elijah Bodish (Massachusetts Institute of Technology)

 

June 12: Shilin Yu (Xiamen University) Duality of nilpotent orbit covers

3:15 – 4:15pm, Evan Williams Theatre

In their study of special unipotent representations for complex semisimple groups, Barbasch and Vogan constructed a duality map between the nilpotent orbits of G and that of its Langlands dual group G^\vee (also discovered by Lusztig and Spaltenstein), which allows them to describe the special unipotent ideals and representations of G in terms of G^\vee. This duality was later generalized by Sommers, Achar and Losev-Mason-Brown-Matvieievskyi.

In collaboration with Lucas Mason-Brown and Dmytro Matvieievskyi (arXiv:2309.14853), we 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.

 

Past Seminars:

2023 Semester 2

2023 Semester 1

2022 Semester 2

2022 Semester 1

2021 Semester 2

2021 Semester 1

2020 Semester 2