Induced representation and Frobenius reciprocityLet us take a pair of compact Lie groups.
Definition:is the space of square integrable functions
taking values in
and satisfying the covariance property:
Schematic notation:
Now we can prove Eq. (5):
The space
is a direct sum of finite-dimensional reps of
. Therefore,
can be interpreted as the multiplicity of
in
. (More precisely, the multiplicity of
)
