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SUMMARY:Unipotent and nilpotent elements in irreducible representations of
  simple algebraic groups
DTSTART:20210519T150000
DTEND:20210519T160000
DTSTAMP:20260920T110411Z
UID:9faa93d365e7ca8734eba220a5c493e0f0c954d2f5ca536072e12a92
CATEGORIES:Conferences - Seminars
DESCRIPTION:Mikko Korhonen\, SUSTech Shenhzen\nFor any group G\, a natural
  way to study a finite-dimensional representation f: G → GL(V) is thro
 ugh the properties of the linear maps f(g): V → V\, for g ∈ G. Wha
 t can we say about these linear maps\, and what do their properties tell u
 s about G and the representation f?\n \nIn this talk\, we consider this q
 uestion and related problems in the context of algebraic groups. Specifica
 lly\, let G be a simple linear algebraic group over an algebraically close
 d field of characteristic p ≥ 0\, and let f: G → GL(V) be a ration
 al irreducible representation. For each unipotent element u ∈ G\, what
  is the Jordan normal form of f(u)? For each nilpotent element e ∈ Lie
 (G)\, what is the Jordan normal form of df(e)?\n \nSolutions to these que
 stion in specific cases have found many applications\, one basic motivatio
 n being in the problem of determining the conjugacy classes of unipotent e
 lements contained in maximal subgroups of simple algebraic groups. In char
 acteristic zero\, there is a fairly good answer by results of Jacobson-Mor
 ozov-Kostant\, and the solutions in the unipotent case and the nilpotent c
 ase are essentially the same. I will focus on the case of positive charact
 eristic p > 0\, where much less is known and few general results are avail
 able. When G is simple of exceptional type\, computations due to R. Lawthe
 r and D. Stewart describe the Jordan normal form of f(u) and df(e) when V 
 is of minimal dimension (adjoint and minimal modules). I will discuss some
  recent results\, mostly focusing on the case where G is simple of classic
 al type.\n\nPasscode: 594961\n 
LOCATION:https://epfl.zoom.us/j/61700695945
STATUS:CONFIRMED
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