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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.10182 |
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| _version_ | 1866909579052318720 |
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| author | Yang, Danting Chen, Xueqing Ding, Ming Xu, Fan |
| author_facet | Yang, Danting Chen, Xueqing Ding, Ming Xu, Fan |
| contents | Let $Q$ be an affine quiver of type $A_2^{(1)}$. We explicitly construct the cluster multiplication formulas for the quantum cluster algebra of $Q$ with principal coefficients. As applications, we obtain: (1)\ an exact expression for every quantum cluster variable as a polynomial in terms of the quantum cluster variables in clusters which are one-step mutations from the initial cluster; (2)\ an explicit bar-invariant positive $\mathbb{ZP}$-basis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10182 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit cluster multiplication formulas for the quantum cluster algebra of type $A_2^{(1)}$ Yang, Danting Chen, Xueqing Ding, Ming Xu, Fan Quantum Algebra Representation Theory Let $Q$ be an affine quiver of type $A_2^{(1)}$. We explicitly construct the cluster multiplication formulas for the quantum cluster algebra of $Q$ with principal coefficients. As applications, we obtain: (1)\ an exact expression for every quantum cluster variable as a polynomial in terms of the quantum cluster variables in clusters which are one-step mutations from the initial cluster; (2)\ an explicit bar-invariant positive $\mathbb{ZP}$-basis. |
| title | Explicit cluster multiplication formulas for the quantum cluster algebra of type $A_2^{(1)}$ |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2504.10182 |