# Q-systems as cluster algebras II: Cartan matrix of finite type and the polynomial property - Mathematics > Representation Theory

Q-systems as cluster algebras II: Cartan matrix of finite type and the polynomial property - Mathematics > Representation Theory - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We define the cluster algebra associated with the Q-system for theKirillov-Reshetikhin characters of the quantum affine algebra $U q\hat{\g}$for any simple Lie algebra g, generalizing the simply-laced case treated inKedem 2007. We describe some special properties of this cluster algebra, andexplain its relation to the deformed Q-systems which appeared on our proof ofthe combinatorial-KR conjecture. We prove that the polynomiality of the clustervariables in terms of the initial cluster seeds-, including solutions of theQ-system, is a consequence of the Laurent phenomenon and the boundaryconditions. We also give a formulation of both Q-systems and generalizedT-systems as cluster algebras with coefficients. This provides a proof of thepolynomiality of solutions of generalized T-systems with appropriate boundaryconditions.

Autor: Philippe Di Francesco, Rinat Kedem

Fuente: https://arxiv.org/