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
收藏
页码：119 / 149
页数：31
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