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Loop Groups, Clusters, Dimers and Integrable Systems

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

Abstract

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.

Keywords

Partition Function Line Bundle Bipartite Graph Poisson Bracket Poisson Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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