Capelli type identities on certain scalar generalized Verma modules, II

Dedicated to Professor Ryoshi Hotta on his sixtieth birthday

Abstract

In the preceding paper we gave an analogue of the Capelli identity for relative invariants in Hermitian symmetric settings, and the analogue was constructed on scalar generalized Verma modules. In this paper we give an analogue of the Capelli identity of lower degrees. This analogue contains non-principal minors in contrast with the original Capelli identity.