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

20 Mar Jiuzu Hong (U North Carolina at Chapel Hill) Global Schubert varieties of parahoric Bruhat-Tits group schemes

Abstract: Global Schubert varieties of parahoric BT group schemes were introduced by Xinwen Zhu in his proof of the coherence conjecture of Pappas-Rapoport. These global Schubert varieties provide flat families relating spherical Schubert varieties in affine Grassmannians and other Schubert varieties or their unions in partial affine flag varieties. In this talk, I will talk about line bundles over global Schubert varieties and their equivariant structures, along with some applications. This talk will be based on the joint work with Huanhuan Yu.

27 Mar Jingren Chi (Morningside Center CAS)

3 Apr Yau Wing Li (Melbourne)

10 Apr Peter McNamara (Melbourne)

Past 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) 1:15pm (Note unusual time!)

A chromatic decomposition of the equivariant cohomology of Grassmannians

Abstract: In 2014 George Lusztig asked if there are “higher generations of quantum groups” that further extend the approximation of the representation theory of algebraic groups in positive characteristics by quantum groups at roots of unity. One approach towards an answer is to employ cohomology theories of higher chromatic height (quantum groups correspond in a precise way to height 1, the modular representation theory to height infinity). So far there is no definition of these higher generation quantum groups, yet I would like to report on recent progress towards a solution in type A1. This is joint work with Yaping Yang and Gufang Zhao.