SUSY Young diagrammsTheory of finite-dimensional representations of is rather nontrivial. They are generally speaking not semisimple, which means that the representation typically is not irreducible, and cannot be decomposed into irreducible representations.An example of non-semisimplicity is the -deformation representation which we described in the beginning of the talk. Consider these representations:
(the last embedding given by ). These invariant subspace do not have invariant complements.
However, there are many finite dimensional irreducible representations.
Irreducible finite dimensional representations are given by SUSY Young diagramms.