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arXiv · 2302.04020

On the polynomiality conjecture of cluster realization of quantum groups

Ivan Chi-Ho Ip·Jeff York Ye
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Abstract

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.

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Ivan Chi-Ho Ip, Jeff York Ye. 2023-02-08. On the polynomiality conjecture of cluster realization of quantum groups. https://arxiv.org/abs/2302.04020

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