| Title:
|
On the composition structure of the twisted Verma modules for $\mathfrak{sl}(3,\mathbb{C})$ (English) |
| Author:
|
Křižka, Libor |
| Author:
|
Somberg, Petr |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
51 |
| Issue:
|
5 |
| Year:
|
2015 |
| Pages:
|
315-329 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra $\mathfrak{sl}(3, \mathbb{C})$, including the explicit structure of singular vectors for both $\mathfrak{sl}(3, \mathbb{C})$ and one of its Lie subalgebras $\mathfrak{sl}(2, \mathbb{C})$, and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as ${D}$-modules on the Schubert cells in the full flag manifold for $\mathop {\rm SL} \nolimits (3, \mathbb{C})$. (English) |
| Keyword:
|
Lie algebra $\mathfrak{sl}(3,\mathbb{C})$ |
| Keyword:
|
twisted Verma modules |
| Keyword:
|
composition structure |
| Keyword:
|
$\mathcal{D}$-modules |
| MSC:
|
22E47 |
| MSC:
|
33C45 |
| MSC:
|
53A30 |
| MSC:
|
58J70 |
| idZBL:
|
Zbl 06537733 |
| idMR:
|
MR3449111 |
| DOI:
|
10.5817/AM2015-5-315 |
| . |
| Date available:
|
2016-01-11T10:11:28Z |
| Last updated:
|
2017-02-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144773 |
| . |
| Reference:
|
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| Reference:
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