Why there is nothing inof
Let us study the representations of SUGRA field configurations. Bosonic SUGRA fields are various tensor fields. Let us for a moment forget about the equations of motion, and even about the gauge transformations. Under the algebra of rotations of the, the SUGRA tensor fields form some representation
. We observe:
A tensor field transforms in some representationof the little algebra
and the corresponding component of
is the so-called “induced representation”:
The Frobenius reciprocity is a relation between the intertwining operators:Let us pause and understand this relation a bit better.