| Title:
|
The F-method and a branching problem for generalized Verma modules associated to $({\mathrm{Lie~}G_2},{\operatorname{so}(7)})$ (English) |
| Author:
|
Milev, Todor |
| Author:
|
Somberg, Petr |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
49 |
| Issue:
|
5 |
| Year:
|
2013 |
| Pages:
|
317-332 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
generalized Verma modules |
| Keyword:
|
conformal geometry in dimension $5$ |
| Keyword:
|
exceptional Lie algebra ${\mathrm{Lie~}G_2}$ |
| Keyword:
|
F-method |
| Keyword:
|
branching problem |
| MSC:
|
13C10 |
| MSC:
|
17B10 |
| MSC:
|
22E47 |
| idZBL:
|
Zbl 06383794 |
| idMR:
|
MR3159331 |
| DOI:
|
10.5817/AM2013-5-317 |
| . |
| Date available:
|
2014-01-16T11:21:10Z |
| Last updated:
|
2015-03-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143556 |
| . |
| Reference:
|
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| Reference:
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[15] Milev, T., Somberg, P.: The branching problem for generalized Verma modules, with application to the pair $(\operatorname{so}(7), \operatorname{Lie}\, G_2)$.http://xxx.lanl.gov/abs/1209.3970. |
| . |
