The F-method and a branching problem for generalized Verma modules associated to $({\mathrm{Lie~}G_2},{\operatorname{so}(7)})$
2013
Abstrakt
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 $\mathrm{Lie~}G_2\stackrel{i}{\hookrightarrow}{so(7)}$, and generalized conformal ${so(7)}$-Verma modules of scalar type.
As a result, we classify the $i(\LieGtwo) \cap \gop$-singular vectors for this class of $so(7)$-modules.