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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2025-01-01
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| 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. |
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| ISSN: | 2050-5094 |