The restriction of simple modules of simple Lie algebras with respect to symmetric pairs is nor very simple, and I will discuss some wild feature together with a criterion of ''discrete decomposability'' as a nice feature.As its application, I plan to propose a new method to obtain Cohen-Rankin operators for holomorphic automorphic forms and Juhl's conformally equivariant differential operators together with their generalizations.
© Toshiyuki Kobayashi