Jacobi-Trudi identity and Drinfeld functor for super Yangian
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866908315380875264 |
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| author | Lu, Kang Mukhin, Evgeny |
| author_facet | Lu, Kang Mukhin, Evgeny |
| contents | We show that the quantum Berezinian which gives a generating function of the integrals of motions of XXX spin chains associated to super Yangian $\mathrm{Y}(\mathfrak{gl}_{m|n})$ can be written as a ratio of two difference operators of orders $m$ and $n$ whose coefficients are ratios of transfer matrices corresponding to explicit skew Young diagrams.
In the process, we develop several missing parts of the representation theory of $\mathrm{Y}(\mathfrak{gl}_{m|n})$ such as $q$-character theory, Jacobi-Trudi identity, Drinfeld functor, extended T-systems, Harish-Chandra map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_15573 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Jacobi-Trudi identity and Drinfeld functor for super Yangian Lu, Kang Mukhin, Evgeny Quantum Algebra Mathematical Physics Representation Theory We show that the quantum Berezinian which gives a generating function of the integrals of motions of XXX spin chains associated to super Yangian $\mathrm{Y}(\mathfrak{gl}_{m|n})$ can be written as a ratio of two difference operators of orders $m$ and $n$ whose coefficients are ratios of transfer matrices corresponding to explicit skew Young diagrams. In the process, we develop several missing parts of the representation theory of $\mathrm{Y}(\mathfrak{gl}_{m|n})$ such as $q$-character theory, Jacobi-Trudi identity, Drinfeld functor, extended T-systems, Harish-Chandra map. |
| title | Jacobi-Trudi identity and Drinfeld functor for super Yangian |
| topic | Quantum Algebra Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2007.15573 |