A note on odd reflections of super Yangian and Bethe ansatz
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866917982956945408 |
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| author | Lu, Kang |
| author_facet | Lu, Kang |
| contents | In a recent paper arXiv:2109.09462, Molev introduced analogues of the odd reflections for the super Yangian $\mathrm{Y}(\mathfrak{gl}_{m|n})$ and obtained a transition rule for the change of highest weights when the parity sequence is altered. In this note, we reproduce the results from a different point of view and discuss their relations with the fermionic reproduction procedure of the XXX-type Bethe ansatz equations introduced in arXiv:1811.11225. We give an algorithm that how the $q$-characters change under the odd reflections. We also take the chance to compute explicitly the $q$-characters of skew representations of $\mathrm{Y}(\mathfrak{gl}_{m|n})$ for arbitrary parity sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_10655 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A note on odd reflections of super Yangian and Bethe ansatz Lu, Kang Quantum Algebra Mathematical Physics Representation Theory In a recent paper arXiv:2109.09462, Molev introduced analogues of the odd reflections for the super Yangian $\mathrm{Y}(\mathfrak{gl}_{m|n})$ and obtained a transition rule for the change of highest weights when the parity sequence is altered. In this note, we reproduce the results from a different point of view and discuss their relations with the fermionic reproduction procedure of the XXX-type Bethe ansatz equations introduced in arXiv:1811.11225. We give an algorithm that how the $q$-characters change under the odd reflections. We also take the chance to compute explicitly the $q$-characters of skew representations of $\mathrm{Y}(\mathfrak{gl}_{m|n})$ for arbitrary parity sequences. |
| title | A note on odd reflections of super Yangian and Bethe ansatz |
| topic | Quantum Algebra Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2111.10655 |