Parabolic inductionThe construction of parabolic induction allows us to construct a representation of the full superalgebrastarting from a representation of the bosonic subalgebra
.
Consider some representationof the bosonic subalgebra:
Let us denotethe 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
.