关于量子群集团实现的多项式猜想
On the polynomiality conjecture of cluster realization of quantum groups
摘要：
本文给出了量子团簇代数$\mathcal{O}_q(\mathcal{X})$的正则元是泛多项式的一个充必要条件。这解决了第一作者关于不同正表示族中量子群生成元的群实现的多项式性的几个问题。
英文摘要：
In this paper, we give a sufficient and necessary condition for a regular element of a quantum cluster algebra $\mathcal{O}_q(\mathcal{X})$ to be universally polynomial. This resolves several conjectures by the first author on the polynomiality of the cluster realization of quantum group generators in different families of positive representations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
