On the polynomiality conjecture of cluster realization of quantum groups

Ivan Chi Ho Ip; Jeff York Ye

doi:10.1016/j.jalgebra.2024.08.031

On the polynomiality conjecture of cluster realization of quantum groups

Ivan Chi Ho Ip^*
, Jeff York Ye

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	119-149
Number of pages	31
Journal	Journal of Algebra
Volume	663
Early online date	17 Sept 2024
DOIs	https://doi.org/10.1016/j.jalgebra.2024.08.031
Publication status	Published - 1 Feb 2025

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Inc.

Keywords

Quantum groups
Positive representations
Cluster algebra
Sign coherence

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10.1016/j.jalgebra.2024.08.031

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title = "On the polynomiality conjecture of cluster realization of quantum groups",

abstract = "In this paper, we give a sufficient and necessary condition for a regular element of a quantum cluster algebra Oq(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.",

keywords = "Quantum groups, Positive representations, Cluster algebra, Sign coherence",

author = "Ip, \{Ivan Chi Ho\} and Ye, \{Jeff York\}",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Inc.",

year = "2025",

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day = "1",

doi = "10.1016/j.jalgebra.2024.08.031",

language = "English",

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T1 - On the polynomiality conjecture of cluster realization of quantum groups

AU - Ip, Ivan Chi Ho

AU - Ye, Jeff York

PY - 2025/2/1

Y1 - 2025/2/1

N2 - In this paper, we give a sufficient and necessary condition for a regular element of a quantum cluster algebra Oq(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.

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

KW - Quantum groups

KW - Positive representations

KW - Cluster algebra

KW - Sign coherence

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001325200500001

UR - https://openalex.org/W4402556994

U2 - 10.1016/j.jalgebra.2024.08.031

DO - 10.1016/j.jalgebra.2024.08.031

M3 - Journal Article

SN - 0021-8693

VL - 663

SP - 119

EP - 149

JO - Journal of Algebra

JF - Journal of Algebra

ER -

On the polynomiality conjecture of cluster realization of quantum groups

Abstract

Bibliographical note

Keywords

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