Abstract:
Given a representation of a group G, one can always define a representation
of a subgroup H of G, by simply restricting the action of the group to the subgroup.
This defines a functor between the categories of representations Rep(G) and Rep(H).
This functor has left and right adjoints, which we respectively call coinduction
and induction functors. The adjunction between induction and restriction is called
Frobenius reciprocity. In this talk we investigate the existence of induction and
coinduction functors in three categories of continuous representations of
a topological group G: discrete, linear complete and compact, and give variants
of Frobenius reciprocity there.