Cluster X-varieties for dual Poisson-Lie groups II
Representation Theory
2010-06-24 v1 Combinatorics
Symplectic Geometry
Abstract
In the prequel of this paper, we have associated a family of cluster X-varieties to the dual Poisson-Lie group(G*,\pi_*) of (G,\pi_G) when (G,\pi_G) is a complex semi-simple Lie group of adjoint type, given with the standard Poisson structure \pi_G and \pi_* 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.
Keywords
Cite
@article{arxiv.1006.4583,
title = {Cluster X-varieties for dual Poisson-Lie groups II},
author = {Renaud Brahami},
journal= {arXiv preprint arXiv:1006.4583},
year = {2010}
}