A discrete Fourier transform associated with the affine Hecke algebra
  We introduce an explicit representation of the double affine Hecke algebra (of type $A_1$) at $q=1$ that gives rise to a periodic counterpart of a well-known Fourier transform associated with the affine Hecke algebra. 
J. F. van Diejen, E. Emsiz
math.RT math-ph math.MP