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Overgroups of regular elements

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If you have a question about this talk, please contact David Craven.

We report on recent work with A. Zalesski concerning the study of reductive overgroups of regular elements in reductive algebraic groups.

In the case where the regular element is a regular unipotent element, this work complements the work of Saxl and Seitz, where they classified the maximal positive-dimensional closed subgroups H of a simple algebraic group G, such that H contains a regular unipotent element of G. Our main result on unipotent elements shows that a connected reductive subgroup H containing a regular unipotent element of G does not lie in a proper parabolic subgroup of G.

We will describe the proof of the above result and its application to the study of overgroups of regular unipotent elements. Then we will discuss our current work on overgroups of general regular elements in simple algebraic groups.

This talk is part of the Algebra Seminar series.

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