Loop Groups, Clusters, Dimers and Integrable Systems

  • Vladimir V. Fock
  • Andrey Marshakov
Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)


The main idea of this work is to demonstrate the equivalence of two a priori different methods of construction and description of a wide class of integrable models, and thus, to propose a unified approach for their investigation. In the first, well-known method [24], the phase space is taken as a quotient of double Bruhat cells of a Kac–Moody Lie group, with the Poisson structure defined by a classical r-matrix, and the integrals of motion are just the Ad-invariant functions. The second method was suggested recently by A.


Partition Function Line Bundle Bipartite Graph Poisson Bracket Poisson Structure 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Vladimir V. Fock
    • 1
  • Andrey Marshakov
    • 2
  1. 1.Institut de Recherche Mathématique AvancéeUniversité de StrasbourgStrasbourgFrance
  2. 2.Theory DepartmentLebedev Physics InstituteMoscowRussia

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