• Corpus ID: 238252921

Geometrization of the TUY/WZW/KZ connection

@inproceedings{Biswas2021GeometrizationOT,
  title={Geometrization of the TUY/WZW/KZ connection},
  author={Indranil Biswas and Swarnava Mukhopadhyay and Richard A. Wentworth},
  year={2021}
}

• I. Biswas, S. Mukhopadhyay, R. Wentworth
• Published 1 October 2021
• Mathematics

Given a simple, simply connected, complex algebraic group G, a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over any family of smooth projective curves with marked points was constructed by the authors in an earlier paper. Here, it is shown that the identification between the bundle of nonabelian theta functions and the bundle of WZNW conformal blocks is flat with respect to this connection and the one constructed by Tsuchiya-Ueno-Yamada. As an application, we give a geometric construction of the Knizhnik-Zamolodchikov connection on the trivial bundle over the configuration space of points in the projective line whose typical fiber is the space of invariants of tensor product of representations.