Orthogonal bases for two-parameter quantum groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908625064165376 |
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| author | Martin, Ian Tsymbaliuk, Alexander |
| author_facet | Martin, Ian Tsymbaliuk, Alexander |
| contents | In this note, we construct dual PBW bases of the positive and negative subalgebras of the two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ in classical types, as used in our earlier work arXiv:2407.01450. Following the ideas of Leclerc and Clark-Hill-Wang, we introduce the two-parameter shuffle algebra and relate it to the subalgebras above. We then use the combinatorics of dominant Lyndon words to establish the main results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orthogonal bases for two-parameter quantum groups Martin, Ian Tsymbaliuk, Alexander Representation Theory High Energy Physics - Theory Mathematical Physics Quantum Algebra Exactly Solvable and Integrable Systems In this note, we construct dual PBW bases of the positive and negative subalgebras of the two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ in classical types, as used in our earlier work arXiv:2407.01450. Following the ideas of Leclerc and Clark-Hill-Wang, we introduce the two-parameter shuffle algebra and relate it to the subalgebras above. We then use the combinatorics of dominant Lyndon words to establish the main results. |
| title | Orthogonal bases for two-parameter quantum groups |
| topic | Representation Theory High Energy Physics - Theory Mathematical Physics Quantum Algebra Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2412.06670 |