We give an interpretation of the Cremmer–Gervais r-matrices for
$${\mathfrak{sl}_n}$$
in terms of actions of elements in the rational and trigonometric Cherednik algebras of type GL
2 on certain subspaces of their polynomial representations. This is used to compute the nilpotency index of the Jordanian r-matrices, thus answering a question of Gerstenhaber and Giaquinto. We also give an interpretation of the Cremmer–Gervais quantization in terms of the corresponding double affine Hecke algebra.