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unige:11928 
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Cluster X-varieties for dual Poisson-Lie groups I |
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| Author | ||
| Year | 2010 | |
| Abstract | We associate a family of cluster X-varieties to the dual Poisson-Lie group G* of a complex semi-simple Lie group G of adjoint type given with the standard Poisson structure. This family is described by the W-permutohedron associated to the Lie algebra g of G: vertices being labeled by cluster X-varieties and edges by new Poisson birational isomorphisms, on appropriate seed X-tori, called saltation. The underlying combinatorics is based on a factorization of the Fomin-Zelevinsky twist maps into mutations and other new Poisson birational isomorphisms on seed X-tori called tropicalmutations, associated to an enrichment of the combinatorics on double words of the Weyl group W of G. | |
| Identifiers | arXiv: 1005.5289v1 | |
| Full text | ||
| Structures | ||
| Citation (ISO format) | BRAHAMI, Renaud. Cluster X-varieties for dual Poisson-Lie groups I. 2010. https://archive-ouverte.unige.ch/unige:11928 |
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