Cluster X-varieties for dual Poisson-Lie groups II

Abstract

In the prequel of this paper, we have associated a family of cluster X-varieties to the dual Poisson-Lie group(G*,π_*) of (G,π_G) when (G,π_G) is a complex semi-simple Lie group of adjoint type, given with the standard Poisson structure π_G and π_* is the "dual" Poisson structure defined by the Semenov-Tian-Shansky Poisson bracket on G. We describe here the cluster combinatorics involved into the Artin group action on G* given by the De-Concini-Kac-Procesi Poisson automorphisms.

References in corpus (2)

• The quantum dilogarithm and representations quantum cluster varieties
• Permutohedra, associahedra, and beyond

Cited by in corpus (1)

• Poisson structures compatible with the cluster algebra structure in Grassmannians