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 $c^{\prime }$ which differ by integers, we construct the translation functor from ${\mathbf{H}}_c-Mod$ to ${\mathbf{H}}_{c^{\prime }}-Mod$ 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.

arXiv comment12pt, 51 pages; to appear in Forum Math. Sigma

References in corpus (5)

• Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories, II
• Koszul duality between Higgs and Coulomb categories $\mathcal{O}$
• Derived equivalences for Rational Cherednik algebras
• Coherent sheaves and quantum Coulomb branches I: tilting bundles from integrable systems
• Knizhnik--Zamolodchikov functor for degenerate double affine Hecke algebras : algebraic theory