Fixed points of DT transformations, cluster exponents and degrees of Weyl groups

Abstract

Inspired by a recent work of Y. Mizuno, we show that the DT transformations on a cluster ensemble of finite type admit unique totally positive fixed points, and that the exponents of the linearizations of the DT transformations at the fixed points are precisely the degrees of the Weyl group of the corresponding finite root system.

arXiv commentCorrections of typos and minor changes on references