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We give explicit constructions of some finite-dimensional representations ofgeneralized double affine Hecke algebras (GDAHA) of higher rank using$R$-matrices for $U_q(\mathfrak{sl}_N)$. Our construction is motivated by ananalogous construction of Silvia Montarani in the rational case. Using theDrinfeld-Kohno theorem for Knizhnik-Zamolodchikov differential equations, weprove that the explicit representations we produce correspond to Montarani'srepresentations under a monodromy functor introduced by Etingof, Gan, andOblomkov.

A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank