On the Equilibrium Configuration of the BC-type Ruijsenaars-Schneider System
J.F. van Diejen
TL;DR
This paper demonstrates that the ground-state equilibrium configurations of the BC-type Ruijsenaars-Schneider system are characterized by the zeros of Askey-Wilson polynomials, linking integrable systems with special functions.
Contribution
It establishes a novel connection between the equilibrium states of a specific integrable system and the zeros of Askey-Wilson polynomials, providing new insights into their structure.
Findings
Ground-state configurations correspond to zeros of Askey-Wilson polynomials
Links between integrable systems and special functions are established
Provides a method to determine equilibrium states using polynomial zeros
Abstract
It is shown that the ground-state equilibrium configurations of the trigonometric BC-type Ruijsenaars-Schneider systems are given by the zeros of Askey-Wilson polynomials.
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