English

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}
}
R2 v1 2026-06-21T15:40:07.234Z