Differential-Dunkl Operators and Nonstandard Solutions to the Classical Yang-Baxter Equation

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For every pair of positive coprime integers, m and n, with m<n, there is an associated generalized Cremmer-Gervais r-matrix rₘ,ₙ for the Lie algebra slₙ which provides a nonstandard quasitriangular solution to the classical Yang-Baxter equation. We give an interpretation of rₙ₋₂,ₙ (for n odd) in terms of differential-Dunkl operators related to the polynomial representation of dihedral-type rational Cherednik algebras. Finally, we use this interpretation to partially answer a conjecture of Gerstenhaber and Giaquinto concerning boundary solutions to the classical Yang-Baxter equation.