Derived equivalences for trigonometric double affine Hecke algebras

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{-}{\m...

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Bibliographic Details
Main Author: Wille Liu
Format: Article
Language:English
Published: Cambridge University Press 2025-01-01
Series:Forum of Mathematics, Sigma
Subjects:
Online Access:https://www.cambridge.org/core/product/identifier/S2050509425100595/type/journal_article
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Summary: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.
ISSN:2050-5094