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CATEGORIES:Algebra and Representation Theory Seminar
SUMMARY:The local structure of G-varieties - Ben Martin (A
uckland)
DTSTART;TZID=Europe/London:20131113T163000
DTEND;TZID=Europe/London:20131113T173000
UID:TALK48435AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/48435
DESCRIPTION:Let G be a reductive algebraic group acting on an
affine variety V. A key problem in geometric inva
riant theory is to understand the structure of the
quotient variety V/G and the behaviour of the orb
its and stabilisers. Luna's etale slice theorem i
s a powerful tool: very roughly\, this says that V
is locally isomorphic to GxS\, where S is a subva
riety of V\, and V/G is locally isomorphic to S.
The slice theorem yields information about stabili
sers of points.\n\nUnfortunately\, the hypotheses
necessary to apply the slice theorem do not always
hold. I will discuss some other approaches for s
tudying stabilisers and orbits. I will also brief
ly describe a project (joint with Guralnick\, Lawt
her\, Liebeck\, Saxl and Testerman) to classify th
e irreducible G-modules having no regular G-orbit.
LOCATION:MR12
CONTACT:Christopher Brookes
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