Basic monodromy operator for quantum superalgebra
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912031220695040 |
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| author | Razumov, A. V. |
| author_facet | Razumov, A. V. |
| contents | We derive the explicit form of the basic monodromy operator for the quantum loop superalgebra $\mathrm{U}_q(\mathcal{L}(\mathfrak{sl}_{2|1}))$. Two significant additional results emerge from this derivation: simple expressions for the generating functions of the the images of the root vectors of $\mathrm{U}_q(\mathcal{L}(\mathfrak{sl}_{2|1}))$ under the Jimbo homomorphism and explicit expressions for certain central elements of the quantum superalgebra $\mathrm{U}_q(\mathfrak{gl}_{2|1})$. Furthermore, we establish the relationship between these central elements and those obtained by using the Drinfeld partial trace method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Basic monodromy operator for quantum superalgebra Razumov, A. V. Quantum Algebra Mathematical Physics We derive the explicit form of the basic monodromy operator for the quantum loop superalgebra $\mathrm{U}_q(\mathcal{L}(\mathfrak{sl}_{2|1}))$. Two significant additional results emerge from this derivation: simple expressions for the generating functions of the the images of the root vectors of $\mathrm{U}_q(\mathcal{L}(\mathfrak{sl}_{2|1}))$ under the Jimbo homomorphism and explicit expressions for certain central elements of the quantum superalgebra $\mathrm{U}_q(\mathfrak{gl}_{2|1})$. Furthermore, we establish the relationship between these central elements and those obtained by using the Drinfeld partial trace method. |
| title | Basic monodromy operator for quantum superalgebra |
| topic | Quantum Algebra Mathematical Physics |
| url | https://arxiv.org/abs/2409.11097 |