Abstract
We introduce a family of non-Abelian nonlinear lattices that generalize Coxeter-Toda lattices in GL n and show that matrix Weyl functions can be used to encode the Hamiltonian structure of these lattices, to establish their complete integrability and to explicitly solve them via the matrix generalization of the inverse moment problem.
Mathematics Subject Classification (2000). Primary 47B36; Secondary 37K10.
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Gekhtman, M., Korovnichenko, O. (2011). Matrix Weyl Functions and Non-Abelian Coxeter-Toda Lattices. In: Brändén, P., Passare, M., Putinar, M. (eds) Notions of Positivity and the Geometry of Polynomials. Trends in Mathematics. Springer, Basel. https://doi.org/10.1007/978-3-0348-0142-3_12
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DOI: https://doi.org/10.1007/978-3-0348-0142-3_12
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