Series of Seminars  04 - 25 October 2016

Room : BI A0 448
Tuesday, October 4th
15:00 - 15:50 Michael Livesey

Loewy lengths of blocks with abelian defect groups
We discuss some of the issues associated with bounding Loewy lengths of blocks, particularly those with abelian defect groups. We then go on to give upper and lower bounds, as a function of the defect group, in the p=2 case and conjecture such bounds for larger p.
16:15 - 17:05 Jon Brundan
Equivalences between blocks of Lie (super)algebras
I will talk about the problem of classifying blocks of category O for the general linear Lie superalgebra, both up to Morita equivalence and up to gradable derived equivalence. The analogous problem for a semisimple Lie algebra is usually approached via Soergel’s theory of graded category O. The main point of the talk will be to explain an appropriate substitute in the super case. This comes from the W-algebra associated to the principal nilpotent orbit in g. Categorical Kac-Moody actions in the sense of Rouquier also play a role.

Tuesday, October 11th
15:00 - 15:50 Carolina Vallejo Rodriguez

Detecting local properties in the character table
Let G be a finite group and p a prime number. We discuss local properties of G that can be read off from its character table. In this flavor, we characterize when the principal p-block of the normalizer of a Sylow p-subgroup of G has one simple module for p odd. We also conjecture about the possibility of extending this result to other blocks. This is joint work with G. Navarro and P. H. Tiep.
16:15 - 17:05 Jacques Thévenaz
Representations of finite sets
A correspondence between two finite sets X and Y is a subset of X × Y . One can easily define the composition of correspondences and obtain a category. A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-vector spaces, where k is a field. The simple correspondence functors are parametrized by triples (E, R, V ), where E is a finite set, R is an order relation on E, and V is a simple module for the group algebra kAut(R). The problem of describing the simple correspondence functor S parametrized by (E, R, V ) is not easy, but a formula is obtained for the dimension of each evaluation S(X). The talk will provide an introduction to the subject and a description of various structural results on correspondence functors. This is a joint work with Serge Bouc.

Tuesday, October 18th
15:00 - 15:50 Alessandro Paolini

Quattern groups and characters of finite unipotent groups
Let G be a split nite group of Lie type over Fq, where q is a power of a prime p. The problem of determining the irreducible complex characters of a Sylow p-subgroup U of G has attracted a lot of interest for many years, with motivation going back to the work of Higman in the 1960's. This has applications to the representation theory of G, in particular to determine its decomposition numbers.
I will discuss a joint work with Goodwin, Le and Magaard about the parametrization of the irreducible characters of U when the rank of G is 4 or less, and p is not a very bad prime for G. This is done via a reduction procedure to certain subquotients of U, called quattern groups. In particular, the parameterization in type F4 is "uniform" over all primes p > 3, where all character degrees are powers of q, but this does not happen for the bad prime p = 3.
16:15 - 17:05 Michael Aschbacher
Subgroup lattices in finite groups
I'll discuss several problems about the subgroup structure of finite groups related to the Palfy-Pudlak Question: Is each finite lattice isomorphic to an interval in the subgroup lattice of some finite group?

Tuesday, October 25th
15:00 - 15:50 Adam Thomas

The Jacobson-Morozov Theorem and complete reducibility of Lie subalgebras
The well-known Jacobson--Morozov Theorem states that every nilpotent element of a complex semisimple Lie algebra Lie(G) can be embedded in an sl_2-subalgebra. Moreover, a result of Kostant shows that this can be done uniquely, up to G-conjugacy. Much work has been done on extending these fundamental results to the modular case when G is a reductive algebraic group over an algebraically closed field of characteristic p > 0. I will discuss joint work with David Stewart, proving that the uniqueness statement of the theorem holds in the modular case precisely when p is larger than h(G), the Coxeter number of G. In doing so, we consider complete reducibility of subalgebras of Lie(G) in the sense of Serre/McNinch.
16:15 - 17:05 Bob Oliver
Automorphisms of fusion and linking systems of finite simple groups Pdf file
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