A panorama of representation theory, in celebration of Donna Testerman
Conference in celebration of Donna Testerman
Conference schedule
Tuesday, June 10th 2025
- 14:00-14:15 – Opening remarks
- 14:15-15:15 – Jacques Thévenaz
- 15:15-15:45 – Coffee break
- 15:45-16:45 – Stephen Donkin
- 16:45-17:15 – Coffee break
- 17:15-18:15 – Martin Liebeck
- 19:00 dinner
Wednesday, June 11th 2025
- 09:00-10:00 – Rebecca Waldecker
- 10:00-10:30 – Coffee break
- 10:30-11:30 – Jonathan Gruber
- 11:30-12:00 – Coffee break
- 12:00-13:00 – Meinolf Geck
Titles & Abstracts
Jacques Thévenaz
Title : From correspondences to lattices
Abstract : Let C be the category of finite sets and correspondences and let k be a field. A correspondence functor is a representation of C, that is, a functor from C to the category k-vect of k-vector spaces. By means of an easy procedure, a correspondence functor can be associated to any finite lattice. This provides a strong link between finite lattices and representations of C. The purpose of the talk is to explore some of the interplay between the two subjects.
Stephen Donkin
Title : Greene’s Theorem and ideal of the group algebra of a symmetric group
Abstract : We show that certain factor rings of the group algebra of a symmetric group have natural bases of group elements. These include the factor rings studied by Raghavan, Samuel and Subrahmanyam, [20] and by Doty, [9]. We also give generators for the annihilator of certain permutation modules for symmetric groups.
Martin Liebeck
Title : Isometry groups of norms
Abstract : There are many well-known and important examples of norms on R^n, and each has an isometry group that is a compact subgroup of GL(n,R). A classical question, going back to J Lindenstrauss and others, asks which compact linear groups can occur as the isometry group of some norm. I shall present a necessary and sufficient criterion for this which can be stated in a rather simple way in terms of the orbits of the group. One consequence is that every finite subgroup of GL(n,R) is the isometry group of a norm, an old result of Gordon and Loewy. The criterion leads to other interesting results and questions about compact Lie groups and their representations, which I shall discuss.
Rebecca Waldecker
Title : Classification, community and connections
Abstract : In this talk I will discuss the Classification of Finite Simple Groups from several perspectives, some of which might be unusual.
Jonathan Gruber
Title : Kazhdan-Lusztig equivalence via Soergel bimodules
Abstract : The category of finite-dimensional representations of a complex simple Lie algebra admits two canonical non-semisimple deformations: One is the parabolic BGG category O for an affine Lie algebra, the other is the category of representations of a quantum group at a root of unity. In a landmark result from the 1990s, Kazhdan and Lusztig have established an equivalence between these non-semisimple abelian categories. More recently, Gaitsgory has proposed a conjectural extension of the Kazhdan-Lusztig equivalence to a derived equivalence between the (non-parabolic) BGG category O of the affine Lie algebra and the category of representations of a “mixed” quantum group. In this talk, I will establish a variant of the derived equivalence conjectured by Gaitsgory, involving the principal blocks of the aforementioned categories, by relating the derived categories of these principal blocks to categories of Soergel bimodules. I will also explain how this derived equivalence can be used to recover a (non-derived) variant of the Kazhdan-Lusztig equivalence, again involving the principal blocks.
This is joint work with Peter Fiebig, partly based on recent results of Ivan Losev.
Meinolf Geck
Title : Computer algebra and algebraic groups
Abstract : We show a number of examples where computer algebra methods
and, especially, the CHEVIE system have been helpful in the theory of
reductive algebraic groups. This concerns a whole range of topics,
including conjugacy classes of Weyl groups, Kazhdan-Lusztig cells,
unipotent classes and nilpotent orbits.
Where : Room CM1 517