# Manchester Algebra Seminar - Ben Martin

Dates: | 2 November 2021 |
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Times: | 13:00 - 14:00 |

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