Cartan matrices in the Toda–Darboux chain theory

A. B. Shabat, V. E. Adler

Landau Institute for Theoretical Physics, Chernogolovka, Moscow Oblast, Russia

Abstract: We discuss a one-to-one correspondence between the polynomial first integrals of Hamiltonian systems with exponential interaction and the hyperintegrals of the two-dimensional Toda lattice. We establish formulas for recalculating the corresponding polynomials and some general properties of their algebraic structure.

Keywords: Cartan matrix, polynomial first integral, exponential system.

Received: 07.03.2018

DOI: 10.4213/tmf9564

 English version: Theoretical and Mathematical Physics, 2018, 196:1, 957–964

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