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Angela Pasquale (Université de Lorraine)


Geometric analysis on symplectic spaces and symmetry breaking operators


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 multiplicity-one theorem and Howe correspondence in a purely analytic way.

This is joint work with Mark McKee and Tomasz Przebinda.