Irreducible finite dimensional representations of SU(2) and SO(3) скачать в хорошем качестве

Irreducible finite dimensional representations of SU(2) and SO(3)

Given that the usefulness of Fourier theory stems in part due to the fact that we decomposed function spaces of periodic functions into irreducible modules over the circle group, one naturally asks the question, what are the finite dimensional irreducible modules over other Lie groups? In this video, we answer this question for SU(2) and SO(3) by studying the modules over the corresponding the universal enveloping algebra. The key is the analysis of eigenspaces of a particular element in the Lie algebra which are called weight spaces. We show that the irreducible modules modules are just the homogeneous components of the polynomial ring C[x,y].