After successful completion of the course, students are able to
Let W be 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.
Whiteboard presentation, interspersed with short exercises.
exam
Lineare Algebra