Group symmetry is one of the most fundamental geometrical properties of the real world. It suffices to say that three of the four fundamental types of physical interactions (namely, electromagnetic, weak, and strong) are controlled by symmetries of the first three special unitary groups: U(1), SU(2), and SU(3), respectively. The representation theory of these groups and of some related structures will be considered in the proposed course.
1. Representations of finite groups:
2. Representations of the special unitary group:
3. Representations of the Lie algebra sl(2,C):
1. W. Fulton, J. Harris. Representation Theory. A first course, Springer-Verlag, 1991