The F-method and a branching problem for generalized Verma modules associated to ( Lie G 2 , so ( 7 ) )

Todor Milev; Petr Somberg

Archivum Mathematicum (2013)

  • Volume: 049, Issue: 5, page 317-332
  • ISSN: 0044-8753

Abstract

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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 Lie G 2 ↪ i so ( 7 ) , and generalized conformal so ( 7 ) -Verma modules of scalar type. As a result, we classify the i ( Lie G 2 ) ∩ 𝔭 -singular vectors for this class of so ( 7 ) -modules.

How to cite

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Milev, Todor, and Somberg, Petr. "The F-method and a branching problem for generalized Verma modules associated to $({\mathrm {Lie~}G_2},{\operatorname{so}(7)})$." Archivum Mathematicum 049.5 (2013): 317-332. <http://eudml.org/doc/260830>.

@article{Milev2013,
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 [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.},
author = {Milev, Todor, Somberg, Petr},
journal = {Archivum Mathematicum},
keywords = {generalized Verma modules; conformal geometry in dimension $5$; exceptional Lie algebra $\{\mathrm \{Lie~\}G_2\}$; F-method; branching problem; generalized Verma modules; conformal geometry in dimension 5; exceptional Lie algebra ; F-method; branching problem},
language = {eng},
number = {5},
pages = {317-332},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The F-method and a branching problem for generalized Verma modules associated to $(\{\mathrm \{Lie~\}G_2\},\{\operatorname\{so\}(7)\})$},
url = {http://eudml.org/doc/260830},
volume = {049},
year = {2013},
}

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
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 049
IS - 5
SP - 317
EP - 332
AB - 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.
LA - eng
KW - generalized Verma modules; conformal geometry in dimension $5$; exceptional Lie algebra ${\mathrm {Lie~}G_2}$; F-method; branching problem; generalized Verma modules; conformal geometry in dimension 5; exceptional Lie algebra ; F-method; branching problem
UR - http://eudml.org/doc/260830
ER -

References

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