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SUMMARY:The local structure of G-varieties - Ben Martin (Auckland)
DTSTART:20131113T163000Z
DTEND:20131113T173000Z
UID:TALK48435@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:Let G be a reductive algebraic group acting on an affine varie
 ty V.  A key problem in geometric invariant theory is to understand the st
 ructure of the quotient variety V/G and the behaviour of the orbits and st
 abilisers.  Luna's etale slice theorem is a powerful tool: very roughly\, 
 this says that V is locally isomorphic to GxS\, where S is a subvariety of
  V\, and V/G is locally isomorphic to S.  The slice theorem yields informa
 tion about stabilisers of points.\n\nUnfortunately\, the hypotheses necess
 ary to apply the slice theorem do not always hold.  I will discuss some ot
 her approaches for studying stabilisers and orbits.  I will also briefly d
 escribe a project (joint with Guralnick\, Lawther\, Liebeck\, Saxl and Tes
 terman) to classify the irreducible G-modules having no regular G-orbit.
LOCATION:MR12
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