Shuffle algebras and their integral forms: specialization map approach in types $B_n$ and $G_2$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929306807042048 |
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| author | Hu, Yue Tsymbaliuk, Alexander |
| author_facet | Hu, Yue Tsymbaliuk, Alexander |
| contents | We construct a family of PBWD bases for the positive subalgebras of quantum loop algebras of type $B_n$ and $G_2$, as well as their Lusztig and RTT (for type $B_n$ only) integral forms, in the new Drinfeld realization. We also establish a shuffle algebra realization of these $\mathbb{Q}(v)$-algebras (proved earlier in arXiv:2102.11269 by completely different tools) and generalize the latter to the above $\mathbb{Z}[v,v^{-1}]$-forms. The rational counterparts provide shuffle algebra realizations of positive subalgebras of type $B_n$ and $G_2$ Yangians and their Drinfeld-Gavarini duals. All of this generalizes the type $A_n$ results of arXiv:1808.09536 by the second author. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_00810 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Shuffle algebras and their integral forms: specialization map approach in types $B_n$ and $G_2$ Hu, Yue Tsymbaliuk, Alexander Quantum Algebra Rings and Algebras Representation Theory We construct a family of PBWD bases for the positive subalgebras of quantum loop algebras of type $B_n$ and $G_2$, as well as their Lusztig and RTT (for type $B_n$ only) integral forms, in the new Drinfeld realization. We also establish a shuffle algebra realization of these $\mathbb{Q}(v)$-algebras (proved earlier in arXiv:2102.11269 by completely different tools) and generalize the latter to the above $\mathbb{Z}[v,v^{-1}]$-forms. The rational counterparts provide shuffle algebra realizations of positive subalgebras of type $B_n$ and $G_2$ Yangians and their Drinfeld-Gavarini duals. All of this generalizes the type $A_n$ results of arXiv:1808.09536 by the second author. |
| title | Shuffle algebras and their integral forms: specialization map approach in types $B_n$ and $G_2$ |
| topic | Quantum Algebra Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2305.00810 |