Manchester Algebra Seminar - Ben Martin
|Starts:||13:00 2 Nov 2021|
|Ends:||14:00 2 Nov 2021|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, Current University students|
Speaker: Ben Martin - Aberdeen
Title: Subgroups of reductive groups containing a regular unipotent element
Abstract: Let G be a linear algebraic group over an algebraically closed field k. A major strand of algebraic group theory is to study the subgroup structure of G: can we describe the subgroups H of G (up to conjugacy) and understand how they fit together? The problem becomes more tractable if we put extra hypotheses on H. For instance, we have a good understanding of the set of connected reductive subgroups H when G is simple.
Suppose G is connected and reductive. A subgroup H of G is said to be G-irreducible if it is not contained in any proper parabolic subgroup of G. Recently we proved the following result: if H is a connected reductive subgroup of G that contains a regular unipotent element of G then G is G-irreducible. A similar result was proved by Testerman and Zalesski and later extended by Malle and Testerman. Our proof is short and carries over nicely to the case when H or G is nonconnected. We have also proved analogous results for Lie algebras and finite groups of Lie type. I will discuss these results and sketch the ideas behind the proofs.
This is joint work with Michael Bate and Gerhard Rohrle.
Place: Frank Adams (and to be streamed online*)
- subject to equipment and connection
Tea and biscuits 12:45 in the foyer
Travel and Contact Information
Alan Turing Building