Lie Algebras in Physics 2.

Course description:
The Weyl groups of Lie algebras. Automorphisms of Lie algebras. Affine Lie algebras as central extensions of loop algebras, Virasoro algebra. Finite dimensional irreducible representations of simple Lie algebras. General theory of highest weight modules. Verma modules, Casimirs, character formulas. Tensor products, Clebsch-Gordan coefficients, tensor operators, invariant tensors, Young tableaux. Subalgebras of semisimple Lie algebras. Represetations on function spaces (Peter-Weyl theorem, special functions in relation with Lie groups). Short introductions to supersymmetry and to Hopf algebras (quantum groups).

Recommended Texts:

• de Kerf  E. A. et al: Lie Algebras, Parts I and II, Volumes 1 and 7 in Studies in Mathematical Physics, North-Holland, 1994 and 1997
• Fuchs J., Schweigert C.: Symmetries, Lie Algebras and Representations, CUP, Cambridge, 1997