Abstract:
We study a unitary non irreducible representation U of a semidirect
product G whose normal factor A is abelian and whose homogeneous factor H is a
locally compact second countable group acting on a Riemannian manifold X. The
key ingredient is a C^1 intertwining map between the actions of H on the dual group of A and X. The representation U generalizes the restriction of the metaplectic representation to triangular subgroups of Sp(d,R). For simplicity, we restrict ourselves to the case where A=R^n and X=R^d. We decompose U as a direct integral and obtain necessary and sufficient conditions for its admissible vectors. Many examples are given.
Keywords:
reproducing formula, metaplectic representation, shearlets,
MSC:
22, 28, 43
