Computational Algebra Seminar: de Graaf -- Classifying semisimple orbits of theta-groups

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.