Q-system Cluster Algebras, Paths and Total Positivity

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2010
• Main Authors: di Francesko, P., Kedem, R.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146152
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Q-system Cluster Algebras, Paths and Total Positivity / P. di Francesco, R. Kedem // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 28 назв. — англ.

In the first part of this paper, we provide a concise review of our method of solution of the Ar Q-systems in terms of the partition function of paths on a weighted graph. In the second part, we show that it is possible to modify the graphs and transfer matrices so as to provide an explicit connecti...