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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Unipotent elements in irreducible representations of simple algebraic groups

## Unipotent elements in irreducible representations of simple algebraic groupsAdd to your list(s) Download to your calendar using vCal - Mikko Korhonen (University of Manchester)
- Tuesday 03 March 2020, 11:00-12:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. GRA - Groups, representations and applications: new perspectives Let G be a simple linear algebraic group over an algebraically closed field K of characteristic p ≥ 0. In this talk, I will discuss the following question and some related problems. Let f:G → I(V) be a rational irreducible representation, where I(V) = SL(V), I(V) = Sp(V), or I(V) = SO(V). For each unipotent element u ∈ G, what is the conjugacy class of f(u) in I(V)? Solutions to this question in specific cases have found many applications, one basic motivation being in the problem of determining the conjugacy classes of unipotent elements contained in maximal subgroups of simple algebraic groups. In characteristic zero, there is a fairly good answer by results of Jacobson-Morozov-Kostant. I will focus on the case of positive characteristic p > 0, where much less is known and few general results are available. When G is simple of exceptional type, computations due to Lawther describe the conjugacy class of f(u) in SL(V) in the case where V is of minimal dimension (adjoint and minimal modules). I will discuss some recent results in the case where G is simple of classical type. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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