Derived equivalences for trigonometric double affine Hecke algebras

Abstract The trigonometric double affine Hecke algebra $\mathbf {H}_c$ for an irreducible root system depends on a family of complex parameters c . Given two families of parameters c and $c'$ which differ by integers, we construct the translation functor from $\mathbf {H}_{c}\text{-}{\mathrm{Mod}}$ to $\mathbf {H}_{c'}\text{-}{\mathrm{Mod}}$ and prove that it induces equivalence of derived categories. This is a trigonometric counterpart of a theorem of Losev on the derived equivalences for rational Cherednik algebras.