BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Unipotent and nilpotent elements in irreducible representations of
simple algebraic groups
DTSTART;VALUE=DATE-TIME:20210519T150000
DTEND;VALUE=DATE-TIME:20210519T160000
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
END:VEVENT
END:VCALENDAR