Geodesic
Derived equivalences for trigonometric double affine Hecke algebras
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e100

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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. 
Liu, Wille. Derived equivalences for trigonometric double affine Hecke algebras. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e100. doi: 10.1017/fms.2025.10059
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