It is shown by [Berest-Etingof-Ginzburg](http://arxiv.org/abs/math/0208138) that there exist finite-dimensional irreducible representations of rational Cherednik algebra $H\_c(S\_n)$ of $A\_{n-1}$ type if and only if the deformation parameter $c$ takes the rational numbers of the form $c=m/n$.


Since the rational Cherednik algebra is the rational degeneration of double affine Hecke algebra (DAHA), the question is as follows:



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> **Question:** Are there the corresponding finite-dimensional representations of DAHA? Or is any finite-dimensional representation of DAHA known?
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Finite-dimensional representations of DAHA
I believe that you should consult the book "Double affine Hecke algebras" by Cherednik, more specifically Section 3.7, more specifically Theorem 3.7.2. 


