As an analogy of unitary representation without continuous spectrum (“discrete decomposable representations”), we give a geometric criterion for the property “having non-trivial subrepresentations” in the restriction of Verma modules with respect to reductive symmetric pairs.[ schedule ]As its application, I discuss intertwining operators in parabolic geometry, and in particular, propose a new method (F-method) to produce naturally Juhl's conformally equivariant differential operators and Cohen-Rankin operators in holomorphic automorphic forms, together with their generalizations.
© Toshiyuki Kobayashi