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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2303.14757 |
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| _version_ | 1866909841712218112 |
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| author | Artamonov, D. V. |
| author_facet | Artamonov, D. V. |
| contents | A model of representations of a Lie algebra is a representation which a direct sum of all irreducible finite dimensional representations taken with multiplicity $1$. In the paper an explicit construction of a model of representation for all series of classical Lie algebras is given. The construction does not differ much for different series. The space of the model is constructed as a space of polynomial solutions of a system of partial differential equations. The equations in this system are constructed form relations between minors of matrices from the corresponding Lie group. This system has a simplification which is very close to the GKZ system, that is satisfied by $A$-hypergeometric functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_14757 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Models of representations for classical series of Lie algebras Artamonov, D. V. Representation Theory A model of representations of a Lie algebra is a representation which a direct sum of all irreducible finite dimensional representations taken with multiplicity $1$. In the paper an explicit construction of a model of representation for all series of classical Lie algebras is given. The construction does not differ much for different series. The space of the model is constructed as a space of polynomial solutions of a system of partial differential equations. The equations in this system are constructed form relations between minors of matrices from the corresponding Lie group. This system has a simplification which is very close to the GKZ system, that is satisfied by $A$-hypergeometric functions. |
| title | Models of representations for classical series of Lie algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2303.14757 |