Finite-dimensional irreducible representations of the quantum superalgebra \(U_ q[gl(n/1)]\) (Q1180368)
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scientific article; zbMATH DE number 25678
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite-dimensional irreducible representations of the quantum superalgebra \(U_ q[gl(n/1)]\) |
scientific article; zbMATH DE number 25678 |
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Finite-dimensional irreducible representations of the quantum superalgebra \(U_ q[gl(n/1)]\) (English)
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27 June 1992
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It is shown that every finite-dimensional irreducible representation of the Lie superalgebra \(gl(n/1)\) can be deformed to an irreducible representation of the quantum supergroup \(U_ q(gl(n/1))\), provided \(q\) is not a root of unity. The results are extended to all Kac modules, which in the atypical cases remain irreducible after deformation. The action of the generators in the Gelfand-Zetlin basis is given explicitly. An analogue of the PBW theorem is proved.
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Poincaré-Birkhoff-Witt theorem
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irreducible representations
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quantized Lie superalgebra
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quantum supergroup
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