Basic Representation theory
This is an introduction to representation theory. Upon completion of this course student will know enough to understand classical applications and will be ready to take more advanced courses leading to modern problems and applications of representation theory. In more detail, the aims are to learn
- common notions and problems of representation theory;
- various instruments for dealing with finite-dimensional representations of finite groups: intertwining operators, characters, Maschke's and Burnside's theorems;
- representations of ring and algebra in a particular case of group ring and algebra.
- representations of symmetric group and related algebraic and combinatorial constructions: Young diagrams and tableau, Young symmetrizers;
- basics of Lie algebras and their representations;
- representations of sl_2(C).