The local structure of G-varieties

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• Ben Martin (Auckland)
• Wednesday 13 November 2013, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Christopher Brookes.

Let G be a reductive algebraic group acting on an affine variety V. A key problem in geometric invariant theory is to understand the structure of the quotient variety V/G and the behaviour of the orbits and stabilisers. 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 information about stabilisers of points.

Unfortunately, the hypotheses necessary to apply the slice theorem do not always hold. I will discuss some other approaches for studying stabilisers and orbits. I will also briefly describe a project (joint with Guralnick, Lawther, Liebeck, Saxl and Testerman) to classify the irreducible G-modules having no regular G-orbit.

This talk is part of the Algebra and Representation Theory Seminar series.

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