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,πG) when (G,πG) is a complex semi-simple Lie group of adjoint type, given with the standard Poisson structure πG 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.
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