Tensor products, Fusion rules and su(2) Representations

Sammanfattning:

In this master thesis I have looked on two different kinds of representations of the Lie algebras su(2) and sl(2), and the tensor products of the representations.

In the first case I looked at a tensor product involving a representation similar to one that appears in an article by A. van Tonder. This representation and tensor product was investigated mainly to get a good comprehension in the subject and to understand some of the problems that can arise.

In the other case, which is the main problem in this thesis, I looked at a tensor product and representations that appears in an article by M. R. Gaberdiel. Here we deal with a tensor product of representations of su(2) with a specific value for the level at k = -4/3 and a specific eigenvalue of the Casimir operator at -2/9. This was done in the frame of finite dimensional Lie algebra and affine Lie algebra and not in the case of fusion rules as in the article by M. R. Gaberdiel.

In both cases some of the calculations where done from in situ and the investigation of the representations behaviour due to the step operators, theirs eigenvalue and theirs weight system.

Results and conclusions of the investigations are discussed in the last part of this thesis.