Geodesic
The F-method and a branching problem for generalized Verma modules associated to $({\mathrm{Lie~}G_2},{\operatorname{so}(7)})$
Archivum mathematicum, Tome 49 (2013) no. 5, pp. 317-332.

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The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras $\mathrm{Lie~}G_2\stackrel{i}{\hookrightarrow }{\operatorname{so}(7)}$, and generalized conformal ${\operatorname{so}(7)}$-Verma modules of scalar type. As a result, we classify the $i({\mathrm{Lie~}G_2}) \cap {\mathfrak{p}}$-singular vectors for this class of $\operatorname{so}(7)$-modules.
DOI : 10.5817/AM2013-5-317
Classification : 13C10, 17B10, 22E47
Keywords: generalized Verma modules; conformal geometry in dimension $5$; exceptional Lie algebra ${\mathrm{Lie~}G_2}$; F-method; branching problem 
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     title = {The {F-method} and a branching problem for generalized {Verma} modules associated to $({\mathrm{Lie~}G_2},{\operatorname{so}(7)})$},
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Milev, Todor; Somberg, Petr. The F-method and a branching problem for generalized Verma modules associated to $({\mathrm{Lie~}G_2},{\operatorname{so}(7)})$. Archivum mathematicum, Tome 49 (2013) no. 5, pp. 317-332. doi : 10.5817/AM2013-5-317. http://geodesic.mathdoc.fr/articles/10.5817/AM2013-5-317/

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