The F-method and a branching problem for generalized Verma modules associated to $({\LieGtwo},{so(7)})$

Abstract: The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in \cite{ms}. In the present article, we employ the recently developed F-method, \cite{KOSS1}, \cite{KOSS2} to the couple of non-compatible Lie algebras $({\LieGtwo},{so(7)})$, and generalized conformal ${so(7)}$-Verma modules of scalar type. As a result, we classify the $\LieGtwo \cap \gop'$-singular vectors for this class of $so(7)$-modules.