The dual representation to the induced representation
is called
coinduced representation
and denoted correspondingly:
(9)
The notation:
-invariant linear maps
from 
to 
.
(In my notations, the action of
on 
in (9) is by the
right multiplication on the element of .)
is dual to
in the following sense:
Indeed, using the “home-made” notation
we find:
Indeed, using the “home-made” notation