University of Illinois Urbana-Champaign

Generalized Bäcklund-Darboux transformations for Coxeter-Toda systems on simple Lie groups

Lin, Mingyan Simon

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https://hdl.handle.net/2142/113186

Description

Title
Generalized Bäcklund-Darboux transformations for Coxeter-Toda systems on simple Lie groups
Author(s)
Lin, Mingyan Simon
Issue Date
2021-07-15
Director of Research (if dissertation) or Advisor (if thesis)
Kedem, Rinat
Doctoral Committee Chair(s)
Di Francesco, Philippe
Committee Member(s)
  • Yong, Alexander
  • Gekhtman, Michael
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Cluster algebras
  • Integrable systems
Abstract
In the first part of this thesis, we construct generalized Bäcklund-Darboux transformations between two Coxeter-Toda systems on simple Lie groups from a cluster algebraic prospective, using the cluster structure on Coxeter double Bruhat cells developed by Fock-Goncharov, Gekhtman et al. and Williams, thereby generalizing the construction developed by Gekhtman et al. We will then show that these generalized Backlund-Darboux transformations preserve Hamiltonian flows generated by the restriction of the trace function of any representation of the simple Lie group. In the second part of this thesis, we develop network formulations of the Coxeter-Toda Hamiltonians for the classical Lie groups, and use these network formulations to obtain combinatorial formulas for the conserved quantities of certain Q-systems.
Graduation Semester
2021-08
Type of Resource
Thesis
Permalink
http://hdl.handle.net/2142/113186
Copyright and License Information
Copyright 2021 Mingyan Lin

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