Generalized Casimir Operators for Lie Superalgebras
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866913395144392704 |
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| author | Rao, S. Eswara |
| author_facet | Rao, S. Eswara |
| contents | In this paper, we define generalized Casimir operators for a loop contragredient Lie superalgebra and prove that they commute with the underlying Lie superalgebra. These operators have applications in the decomposition of tensor product modules. We further introduce the notion of generalized Gelfand invariants for the loop general linear Lie superalgebra and show that they also commute with the underlying Lie superalgebra. These operators when applied to a highest weight vector in a tensor product module again induces a new highest weight vector. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_02133 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Generalized Casimir Operators for Lie Superalgebras Rao, S. Eswara Representation Theory In this paper, we define generalized Casimir operators for a loop contragredient Lie superalgebra and prove that they commute with the underlying Lie superalgebra. These operators have applications in the decomposition of tensor product modules. We further introduce the notion of generalized Gelfand invariants for the loop general linear Lie superalgebra and show that they also commute with the underlying Lie superalgebra. These operators when applied to a highest weight vector in a tensor product module again induces a new highest weight vector. |
| title | Generalized Casimir Operators for Lie Superalgebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2011.02133 |