On the universal ellipsitomic KZB connection
In: Selecta Mathematica (New Series) Selecta Mathematica (New Series), Springer Verlag, 2020, 26, pp.73. ⟨10.1007/s00029-020-00601-6⟩ Selecta Mathematica Selecta Mathematica (New Series), 2020, 26, pp.73. ⟨10.1007/s00029-020-00601-6⟩; (2019-08-11)
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Zugriff:
We construct a twisted version of the genus one universal Knizhnik-Zamolodchikov-Bernard (KZB) connection introduced by Calaque-Enriquez-Etingof, that we call the ellipsitomic KZB connection. This is a flat connection on a principal bundle over the moduli space of $\Gamma$-structured elliptic curves with marked points, where $\Gamma=\mathbb{Z}/M\mathbb{Z}\times\mathbb{Z}/N\mathbb{Z}$, and $M,N\geq1$ are two integers. It restricts to a flat connection on $\Gamma$-twisted configuration spaces of points on elliptic curves, which can be used to construct a filtered-formality isomorphism for some interesting subgroups of the pure braid group on the torus. We show that the universal ellipsitomic KZB connection realizes as the usual KZB connection associated with elliptic dynamical $r$-matrices with spectral parameter, and finally, also produces representations of cyclotomic Cherednik algebras.
Comment: 50 pages. Main changes in v3 (final version): updated biblio (unused refs deleted), shift in numbering in Section 3 (to make it agree with the published version), and minor change in glossary of notation (to make it consistent with the body of the text) Also available at https://rdcu.be/b822g
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On the universal ellipsitomic KZB connection
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Autor/in / Beteiligte Person: | Gonzalez, Martin ; Calaque, Damien ; Institut Montpelliérain Alexander Grothendieck (IMAG) ; Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS) ; Institut Universitaire de France (IUF) ; Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.) ; Max Planck Institute for Mathematics (MPIM) ; Max-Planck-Gesellschaft ; Institut de Mathématiques de Marseille (I2M) ; Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU) ; Institut Universitaire de FranceANR, SAT ; ANR-14-CE25-0008,SAT,Structures supérieures en Algèbre et Topologie(2014) ; Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS) |
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Quelle: | Selecta Mathematica (New Series) Selecta Mathematica (New Series), Springer Verlag, 2020, 26, pp.73. ⟨10.1007/s00029-020-00601-6⟩ Selecta Mathematica Selecta Mathematica (New Series), 2020, 26, pp.73. ⟨10.1007/s00029-020-00601-6⟩; (2019-08-11) |
Veröffentlichung: | 2019 |
Medientyp: | unknown |
ISSN: | 1022-1824 (print) ; 1420-9020 (print) |
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