On the polynomiality conjecture of cluster realization of quantum groups

被引：0

作者：

Ip, Ivan Chi-Ho ^{[1
]}

Ye, Jeff York ^{[2
]}

机构：

[1] Hong Kong Univ Sci & Technol, Dept Math, Hong Kong, Peoples R China

[2] Natl Univ Singapore, Dept Math, Singapore, Singapore

来源：

JOURNAL OF ALGEBRA | 2025年 / 663卷

关键词：

Quantum groups; Positive representations; Cluster algebra; Sign coherence; POSITIVE REPRESENTATIONS;

D O I：

10.1016/j.jalgebra.2024.08.031

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we give a sufficient and necessary condition for a regular element of a quantum cluster algebra O q ( 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.

引用

页码：119 / 149

页数：31

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