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

[21] Differential operator realization of braid group action on ıquantum groups
Fan, Zhaobing
Geng, Jicheng
Han, Shaolong
JOURNAL OF MATHEMATICAL PHYSICS, 2023, 64 (10)
[22] Thomassen's Conjecture Implies Polynomiality of 1-Hamilton-Connectedness in Line Graphs
Kuzel, Roman
Ryjacek, Zdenek
Vrana, Petr
JOURNAL OF GRAPH THEORY, 2012, 69 (04) : 241 - 250
[23] RINGS OF SKEW POLYNOMIALS AND GELFAND-KIRILLOV CONJECTURE FOR QUANTUM GROUPS
IOHARA, K
MALIKOV, F
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 164 (02) : 217 - 237
[24] CERTAIN BILINEAR-FORMS ON QUANTUM GROUPS AND A CONJECTURE OF SCHECHTMAN AND VARCHENKO
ROSSO, M
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1992, 314 (01): : 5 - 8
[25] CLUSTER REALIZATION OF POSITIVE REPRESENTATIONS OF A SPLIT REAL QUANTUM BOREL SUBALGEBRA
Ip, I. C. -H.
THEORETICAL AND MATHEMATICAL PHYSICS, 2019, 198 (02) : 215 - 238
[26] Cluster Realization of Positive Representations of a Split Real Quantum Borel Subalgebra
I. C.-H. Ip
Theoretical and Mathematical Physics, 2019, 198 : 215 - 238
[27] A CONJECTURE ON CLUSTER AUTOMORPHISMS OF CLUSTER ALGEBRAS
Cao, Peigen
Li, Fang
Liu, Siyang
Pan, Jie
ELECTRONIC RESEARCH ARCHIVE, 2019, 27 : 1 - 6
[28] Thomassen's conjecture implies polynomiality of 1-Hamilton-connectedness in line graphs
Kuzel, Roman
Ryjacek, Zdenek
Vrana, Petr
JOURNAL OF GRAPH THEORY, 2012, 69 (03) : 241 - 250
[29] Surgery and bordism groups in quantum partial differential equations. I: The quantum Poincare conjecture
Prastaro, Agostino
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (12) : E502 - E525
[30] POINCARES CONJECTURE IS IMPLIED BY A CONJECTURE ON FREE GROUPS
TRAUB, RD
JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS SECTION B-MATHEMATICAL SCIENCES, 1967, B 71 (2-3): : 53 - +

← 1 2 3 4 5 →