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Article Dans Une Revue Selecta Mathematica (New Series) Année : 2020

On the universal ellipsitomic KZB connection

Résumé

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 for proving the formality of 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.
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Dates et versions

hal-02333596 , version 1 (11-10-2023)

Identifiants

Citer

Damien Calaque, Martin Gonzalez. On the universal ellipsitomic KZB connection. Selecta Mathematica (New Series), 2020, 26, pp.73. ⟨10.1007/s00029-020-00601-6⟩. ⟨hal-02333596⟩
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