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CATEGORIES:Junior Algebra and Number Theory seminar
SUMMARY:Lusztig's unipotent pieces and geometric invariant
theory - Matthew Clarke (Cambridge)
DTSTART;TZID=Europe/London:20110311T140000
DTEND;TZID=Europe/London:20110311T150000
UID:TALK29637AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/29637
DESCRIPTION:Linear algebraic groups are subgroups of the gener
al linear group which are closed under the Zariski
topology. The concept is similar to that of Lie g
roups\, although fields of prime characteristic ar
e admitted\, and indeed arguably provide the most
interesting problems and applications. A very impo
rtant class of linear algebraic groups are reducti
ve groups\, which include all the classical groups
. This talk is concerned with the conjugacy classe
s of unipotent elements in a reductive group\, i.e
. the matrices which have all eigenvalues all equa
l to 1. These classes are very important in many t
opics and we have a nice classification of them wh
en the characteristic of the field is not too smal
l. When it is too small things can get a bit ugly\
, but a unified geometric picture has been propose
d by G. Lusztig in a series of conjectures\, some
of which he proved in a case-by-case manner. In th
is talk I will explain a uniform approach to these
conjectures using geometric invariant theory\, wh
ich has yielded a short case-free proof. This is j
oint work with Professor A. Premet (Manchester).
LOCATION:MR4
CONTACT:Chris Bowman
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