Intertwining operators between holomorphically induced modules
The authors investigate the existence of covariant differential intertwining operators for members in the family of continued holomorphic discrete series for the groups SU(p,q), Sp(n,\({\mathbb{R}})\), \(SO^*(2n)\) and for the exceptional cases \(E_ 6\) and \(E_ 7\). These spaces of intertwining operators are isomorphic to the space of \({\mathfrak g}\)- homomorphisms between generalized Verma modules corresponding to regular integrals. The authors show these spaces are at most one-dimensional and can be computed algorithmically from lower-dimensional cases. For \(E_ 6\) and \(E_ 7\) a brief description of the homomorphisms is made modulo the homomorphisms between certain simpler singular modules.
scientific article; zbMATH DE number 4027781