Seminar

Representation theory seminar 2025 Semester 1

Organisers: Dougal Davis, Kari Vilonen, Ting Xue

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

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

Upcoming Talks

31 Jan (Friday) 3-5pm: (Note unusual date and time!)

Oscar Kivinen (Aalto University) Shalika germs and localization on Hilbert schemes

Abstract: Shalika’s germ expansion allows us to understand regular semisimple orbital integrals for reductive Lie algebras over non-archimedean local fields in terms of nilpotent orbital integrals. In work with Tsai, we gave an algorithm to compute most orbital integrals and Shalika germs for $gl_n(F)$ . It turns out that the germs admit a canonical t-deformation which is closely related to Macdonald polynomials. This suggests a categorified statement, where the deformed orbital integrals are replaced by coherent sheaves on Hilbert schemes. In this talk, I will explain the non-categorified version and, time permitting, discuss what is currently known about the categorification.

6 Feb Jonathan Gruber (FAU Erlangen-Nürnberg) Tensor structures for affine Lie algebras at positive levels

Abstract: An affine Lie algebra g is a central extension of the loop algebra of a complex simple Lie algebra, and a g-module is said to have (relative) level k if the canonical central element acts by the scalar k-h, where h is the dual Coxeter number. For all levels k that are not positive rational or zero, Kazhdan and Lusztig have defined a braided monoidal structure on a parabolic BGG category O of g-modules of level k. In this talk, I will explain the definition of a braided monoidal structure on the category O at positive rational levels, via a monoidal enhancement of Brundan and Stroppel’s semi-inifnite Ringel duality.
This is based on joint work with Johannes Flake and Robert McRae.

13 Feb Peter Fiebig (FAU Erlangen-Nürnberg)

20 Mar Jiuzu Hong (U North Carolina at Chapel Hill)