Type: Seminar

Distribution: World

Expiry: 14 Apr 2011

Auth: billu@daumier.maths.usyd.edu.au

Speaker: Willem de Graaf Title: Classifying semisimple orbits of theta-groups Time & Place: 3:05-4pm, Thursday 14 April, Carslaw 535 Abstract: Theta-groups were introduced by Vinberg in the 70-s. They are a class of reductive algebraic groups for which there is a well-developed theory dealing with their orbits, allowing classifications of them. In this talk I will describe what theta-groups are, and then concentrate on the semisimple orbits. Vinberg showed that every semisimple orbit has a point in a subspace called Cartan subspace, two points of a Cartan subspace are conjugate iff they are conjugate under a certain complex reflection group, called the little Weyl group, and different orbits of the little Weyl group are separated by invariants. I will describe some computational techniques for computing a Cartan subspace and the little Weyl group, and the results obtained with them, using Magma.