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Title:Generalized Bäcklund-Darboux transformations for Coxeter-Toda systems on simple Lie groups
Author(s):Lin, Mingyan Simon
Director of Research:Kedem, Rinat
Doctoral Committee Chair(s):Di Francesco, Philippe
Doctoral Committee Member(s):Yong, Alexander; Gekhtman, Michael
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(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.
Issue Date:2021-07-15
Rights Information:Copyright 2021 Mingyan Lin
Date Available in IDEALS:2022-01-12
Date Deposited:2021-08

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