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SUMMARY:Unipotent elements in irreducible representations of simple algebr
 aic groups - Mikko Korhonen (University of Manchester)
DTSTART:20200303T110000Z
DTEND:20200303T120000Z
UID:TALK140077@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Let G be a simple linear algebraic group over an algebraically
  closed field K of characteristic p &ge\; 0. In this talk\, I will discuss
  the following question and some related problems.  Let f:G &rarr\; I(V) b
 e a rational irreducible representation\, where I(V) = SL(V)\, I(V) = Sp(V
 )\, or I(V) = SO(V). For each unipotent element u &isin\; G\, what is the 
 conjugacy class of f(u) in I(V)?  Solutions to this question in specific c
 ases have found many applications\, one basic motivation being in the prob
 lem of determining the conjugacy classes of unipotent elements contained i
 n maximal subgroups of simple algebraic groups. In characteristic zero\, t
 here is a fairly good answer by results of Jacobson-Morozov-Kostant. I wil
 l 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 exception
 al 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 simpl
 e of classical type.
LOCATION:Seminar Room 2\, Newton Institute
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