Classification of coadjoint orbits for the maximal unipotent subgroup in the simple group of type F_4
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917197370097664 |
|---|---|
| author | Surkov, Matvey A. |
| author_facet | Surkov, Matvey A. |
| contents | Let N be the maximal unipotent subgroup in the simple algebraic group of type Φ. It naturally acts on the space dual to the Lie algebra n of N, and this action is called coadjoint. Such orbits play the key role in the orbit method of A.A. Kirillov. In this work, we classify the orbits of this action in the case of Φ = F_4 in terms of supports of canonical forms. This means that we will present a set S of linear forms such that for any coadjoint orbit there exists a unique form from S belonging to that orbit. The set of canonical forms will be explicitly described in terms of supports. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19701 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of coadjoint orbits for the maximal unipotent subgroup in the simple group of type F_4 Surkov, Matvey A. Representation Theory Let N be the maximal unipotent subgroup in the simple algebraic group of type Φ. It naturally acts on the space dual to the Lie algebra n of N, and this action is called coadjoint. Such orbits play the key role in the orbit method of A.A. Kirillov. In this work, we classify the orbits of this action in the case of Φ = F_4 in terms of supports of canonical forms. This means that we will present a set S of linear forms such that for any coadjoint orbit there exists a unique form from S belonging to that orbit. The set of canonical forms will be explicitly described in terms of supports. |
| title | Classification of coadjoint orbits for the maximal unipotent subgroup in the simple group of type F_4 |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2504.19701 |