Difference Equations and Pieri Formulas for G2 Type Macdonald Polynomials and Integrability

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We present a second explicit difference equation and—by duality symmetry—a second explicit Pieri formula for the Macdonald polynomials associated with the exceptional root system of type G2, complementing the celebrated difference equation and Pieri formula due to Macdonald. As by-product, we find a complete set of integrals for the corresponding trigonometric Ruijsenaars–Schneider type particle system.

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