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

共 50 条

[1] Cluster realization of Weyl groups and q-characters of quantum affine algebras
Inoue, Rei
LETTERS IN MATHEMATICAL PHYSICS, 2021, 111 (01)
[2] Cluster realization of Weyl groups and q-characters of quantum affine algebras
Rei Inoue
Letters in Mathematical Physics, 2021, 111
[3] Polynomiality of factorizations in reflection groups
Polak, Elzbieta
Ross, Dustin
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2023, 75 (01): : 245 - 266
[4] ON THE BAUM-CONNES CONJECTURE FOR DISCRETE QUANTUM GROUPS WITH TORSION AND THE QUANTUM ROSENBERG CONJECTURE
Arano, Yuki
Skalski, Adam
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149 (12) : 5237 - 5254
[5] Polynomiality of irreducible characters of the symmetric groups
Goryachko E.E.
Journal of Mathematical Sciences, 2011, 174 (1) : 15 - 18
[6] A Wilson line realization of quantum groups
Aamand, Nanna
Kaufman, Dani
LETTERS IN MATHEMATICAL PHYSICS, 2024, 114 (01)
[7] A Wilson line realization of quantum groups
Nanna Aamand
Dani Kaufman
Letters in Mathematical Physics, 114
[8] Experimental Realization of Quantum Teleportation as Cluster Computation
Ukai, Ryuji
Armstrong, Seiji C.
van Loock, Peter
Furusawa, Akira
2009 CONFERENCE ON LASERS AND ELECTRO-OPTICS AND QUANTUM ELECTRONICS AND LASER SCIENCE CONFERENCE (CLEO/QELS 2009), VOLS 1-5, 2009, : 1945 - +
[9] The Berenstein-Zelevinsky quantum cluster algebra conjecture
Goodearl, K. R.
Yakimov, M. T.
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2020, 22 (08) : 2453 - 2509
[10] Realization of ıquantum groups via Δ-Hall algebras
Chen, Jiayi
Lin, Yanan
Ruan, Shiquan
JOURNAL OF ALGEBRA, 2024, 653 : 378 - 403

← 1 2 3 4 5 →