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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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425100595/type/journal_article |
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| author | Wille Liu |
| author_facet | Wille Liu |
| author_sort | Wille Liu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1d69dd44ef3346d68a0e27cb725fe0f0 |
| institution | DOAJ |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-1d69dd44ef3346d68a0e27cb725fe0f02025-08-20T03:12:24ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2025.10059Derived equivalences for trigonometric double affine Hecke algebrasWille Liu0https://ror.org/0120q3031Institute of Mathematics, Academia Sinica, 6F, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Da-an, Taipei 106319, TaiwanThe 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.https://www.cambridge.org/core/product/identifier/S2050509425100595/type/journal_article20C08 |
| spellingShingle | Wille Liu Derived equivalences for trigonometric double affine Hecke algebras Forum of Mathematics, Sigma 20C08 |
| title | Derived equivalences for trigonometric double affine Hecke algebras |
| title_full | Derived equivalences for trigonometric double affine Hecke algebras |
| title_fullStr | Derived equivalences for trigonometric double affine Hecke algebras |
| title_full_unstemmed | Derived equivalences for trigonometric double affine Hecke algebras |
| title_short | Derived equivalences for trigonometric double affine Hecke algebras |
| title_sort | derived equivalences for trigonometric double affine hecke algebras |
| topic | 20C08 |
| url | https://www.cambridge.org/core/product/identifier/S2050509425100595/type/journal_article |
| work_keys_str_mv | AT willeliu derivedequivalencesfortrigonometricdoubleaffineheckealgebras |