

Angela Pasquale (Université de Lorraine)
Title:
Geometric analysis on symplectic spaces and symmetry breaking operators
Abstract:
We study orbital integrals on a symplectic space under the action of a dual pair guided by
Hermann Weyl’s integration formula. These orbital integrals are necessary to understand
the Weyl symbols of the projection operators on the isotopic components under the action
of a compact member of a dual pair. These projection operators are examples of symmetry
breaking operators in the sense of Kobayashi. Our main example will be the dual pair of
two compact unitary groups. In this case, we recover Weyl’s multiplicityone theorem and
Howe correspondence in a purely analytic way.
This is joint work with Mark McKee and Tomasz Przebinda.


