We prove that the global geometric theta-lifting functor for the dual pair is compatible with the Whittaker functors, where is one of the pairs , or . That is, the composition of the theta-lifting functor from to with the Whittaker functor for is isomorphic to the Whittaker functor for .
The existence of a projection onto an ideal I of a commutative group algebra depends on its hull Z(I) ⊆ Ĝ. Existing methods for constructing a projection onto I rely on a decomposition of Z(I) into simpler hulls, which are then reassembled one at a time, resulting in a chain of projections which can be composed to give a projection onto I. These methods are refined and examples are constructed to show that this approach does not work in general. Some answers are also given to previously asked...
We present an example of a complete -bounded topological group which is not -factorizable. In addition, every -set in the group is open, but is not Lindelöf.