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

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{10_5817_AM2013_5_317,
     author = {Milev, Todor and Somberg, Petr},
     title = {The {F-method} and a branching problem for generalized {Verma} modules associated to $({\mathrm{Lie~}G_2},{\operatorname{so}(7)})$},
     journal = {Archivum mathematicum},
     pages = {317--332},
     publisher = {mathdoc},
     volume = {49},
     number = {5},
     year = {2013},
     doi = {10.5817/AM2013-5-317},
     mrnumber = {3159331},
     zbl = {06383794},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2013-5-317/}
}
TY  - JOUR
AU  - Milev, Todor
AU  - Somberg, Petr
TI  - The F-method and a branching problem for generalized Verma modules associated to $({\mathrm{Lie~}G_2},{\operatorname{so}(7)})$
JO  - Archivum mathematicum
PY  - 2013
SP  - 317
EP  - 332
VL  - 49
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2013-5-317/
DO  - 10.5817/AM2013-5-317
LA  - en
ID  - 10_5817_AM2013_5_317
ER  - 
%0 Journal Article
%A Milev, Todor
%A Somberg, Petr
%T The F-method and a branching problem for generalized Verma modules associated to $({\mathrm{Lie~}G_2},{\operatorname{so}(7)})$
%J Archivum mathematicum
%D 2013
%P 317-332
%V 49
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2013-5-317/
%R 10.5817/AM2013-5-317
%G en
%F 10_5817_AM2013_5_317
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

Cité par Sources :