An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Author: Qin, Fan
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211097
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras. Fan Qin. SIGMA 16 (2020), 122, 22 pages

Dual canonical bases are expected to satisfy a certain (double) triangularity property by Leclerc's conjecture. We propose an analogous conjecture for common triangular bases of quantum cluster algebras. We show that a weaker form of the analogous conjecture is true. Our result applies to the d...