Perfect basis theory for quantum Borcherds-Bozec algebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866929338241253376 |
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| author | Fan, Zhaobing Han, Shaolong Kang, Seok-Jin Kim, Young Rock |
| author_facet | Fan, Zhaobing Han, Shaolong Kang, Seok-Jin Kim, Young Rock |
| contents | In this paper, we develop the perfect basis theory for quantum Borcherds-Bozec algebras $U_{q}(\mathfrak g)$ and their irreducible highest weight modules $V(λ)$. We show that the lower perfect graph (resp. upper perfect graph) of every lower perfect basis (resp. upper perfect basis) of $U_{q}^{-}(\mathfrak g)$ (resp. $V(λ)$) is isomorphic to the crystal $B(\infty)$ (resp. $B(λ)$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Perfect basis theory for quantum Borcherds-Bozec algebras Fan, Zhaobing Han, Shaolong Kang, Seok-Jin Kim, Young Rock Quantum Algebra In this paper, we develop the perfect basis theory for quantum Borcherds-Bozec algebras $U_{q}(\mathfrak g)$ and their irreducible highest weight modules $V(λ)$. We show that the lower perfect graph (resp. upper perfect graph) of every lower perfect basis (resp. upper perfect basis) of $U_{q}^{-}(\mathfrak g)$ (resp. $V(λ)$) is isomorphic to the crystal $B(\infty)$ (resp. $B(λ)$). |
| title | Perfect basis theory for quantum Borcherds-Bozec algebras |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2405.05666 |