In this course we will study some of the basics of invariant theory.  The contents is roughly that of Hermann Weyl's classic book The Classical Groups: Their Invariants and Representations.  The presentation will follow the text by Hanspeter Kraft and Claudio Procesi Classical invariant theory, a primer.

Let W ba a (finite dimensional, complex) vector space.  A map f from W to the complex numbers is polynomial, if it is a polynomial in the coordinates with respect to any basis of W.

Let G be a group, eg. the special linear group SL(n) of n x n matrices with determinant 1, and let W be a G-module.  For example, G might act on the n-dimensional complex vector space by ordinary matrix multiplication.  A polynomial function f is invariant, if we have f(g w) = f(w) for all elements of the group g and all vectors w.

Following Hermann Weyl we will thus determine the invariant functions for a few classical groups.

There will be a meeting on Friday, March 8., 10:30 Uhr in the "Tutorenzimmer", DA 07 C22, 7.Stock, Turm A, Freihaus to fix the time slot and any discuss any special needs.

Please submit your preferred time slot for the lectures in this Doodle - if none of the time slots works for you, please leave a comment!

Lineare Algebra