Parabolic inductionThe construction of parabolic induction allows us to construct a representation of the full superalgebra starting from a representation of the bosonic subalgebra .Consider some representation of the bosonic subalgebra:

Let us denote the parabolic subalgebra of :We can consider as a representation of the parabolic subalgebra, if we postulate that acts by zero.

So, is now a representation of .