Relativistic Toda chain at root of unity

Details Relativistic Toda chain at root of unity Relativistic Toda chain at root of unity

2001-01-15

arxiv.org/abs/nlin/0101024v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX2e, 15 pages; references improved

Scientific paper

We declare briefly several interesting features of the quantum relativistic Toda chain at N-th root of unity. We consider the finite dimensional representation of the Weyl algebra. The origin of the features mentioned is that we consider simultaneously the quantum finite dimensional part and the classical dynamics of N-th powers of Weyl's elements. As the main result, using the technique of Q-operators, we establish a correspondence between the separation of variables in the quantum model and the Baecklund transformations of its classical counterpart.

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