The Gelfand-Tsetlin type base for the algebra $\mathfrak{g}_2$
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_ | 1866908589664239616 |
|---|---|
| author | Artamonov, Dmitry |
| author_facet | Artamonov, Dmitry |
| contents | The paper presents a construction of finite-dimensional irreducible representations of the Lie algebra $\mathfrak{g}_2$. The representation space is constructed as the space of solutions to a certain system of partial differential equations of hypergeometric type, which is closely related to the Gelfand-Kapranov-Zelevinsky systems. This connection allows for the construction of a basis in the representation. The orthogonalization of the constructed basis with respect to the invariant scalar product turns out to be a Gelfand-Tsetlin-type basis for the chain of subalgebras $\mathfrak{g}_2 \supset \mathfrak{sl}_3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11510 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Gelfand-Tsetlin type base for the algebra $\mathfrak{g}_2$ Artamonov, Dmitry Representation Theory The paper presents a construction of finite-dimensional irreducible representations of the Lie algebra $\mathfrak{g}_2$. The representation space is constructed as the space of solutions to a certain system of partial differential equations of hypergeometric type, which is closely related to the Gelfand-Kapranov-Zelevinsky systems. This connection allows for the construction of a basis in the representation. The orthogonalization of the constructed basis with respect to the invariant scalar product turns out to be a Gelfand-Tsetlin-type basis for the chain of subalgebras $\mathfrak{g}_2 \supset \mathfrak{sl}_3$. |
| title | The Gelfand-Tsetlin type base for the algebra $\mathfrak{g}_2$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2510.11510 |