SUSY Young diagramms

The method of Young diagramms allows to construct finite-dimensional representatrions of as ternsor products of the fundamental representation.

SUSY Young diagramms for are more complicated than in the bosonic case, because there are two types of building blocks: fundamental and antifundamental representations. In the bosonic case the antifundamental is constructed from the antisymmetric tensor product of fundamental. But in the SUSY case they are independent.

Let denote the fundamental representation and the antifundamental. To construct irreducible representations, one has to go through the following steps:

  • Take tensor product of some number of fundamental and antifundamental representations:

        

  • Do symmetrization and antisymmetrization separately for and , according to a Young diagramm which we illustrate on the next slide

  • Remove traces