Generalized Casimir operators for Lie superalgebras

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...

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Bibliographic Details
Published in:Journal of mathematical physics 2021-10, Vol.62 (10)
Main Author: Rao, S. Eswara
Format: Article
Language:English
Subjects:
Mathematical analysis
Modules
Operators
Physics
Tensors
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Summary: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 induce a new highest weight vector.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0056538