  We attach elliptic Dunkl operators to an abelian variety with a finite group
action. This generalizes elliptic Dunkl operators for Weyl groups, defined by
Buchstaber, Felder, and Veselov in 1994. We show that these operators commute,
and use them to define representations from category O of elliptic Cherednik
algebras. We also consider the monodromy representations of differential
equations defined by elliptic Dunkl operators, and show that they yield finite
dimensional rrepresentations of generalized double affine Hecke algebras.
