Homological representations of braid groups and KZ connections

Journal of Singularities
volume 5 (2012), 94-108
Proceedings of the International Conference on Singularity Theory and Applications, Hefei, China, July 25-31, 2011

Received 21 December 2011. Received in revised form 10 March 2012.

DOI: 10.5427/jsing.2012.5g

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Abstract:

We give a relation between the homological representations of the braid groups studied by Lawrence, Krammer and Bigelow and the monodromy of the KZ equation with values in the space of null vectors in the tensor product of Verma modules of $sl_2({\mathbf C})$ when the parameters are generic. We also discuss the case of special parameters in relation with integral representations of the space of conformal blocks by hypergeometric integrals.

Author(s) information:

Toshitake Kohno
IPMU, Graduate School of Mathematical Sciences
The University of Tokyo
3-8-1 Komaba, Meguro-ku
Tokyo 153-8914 Japan
email: kohno@ms.u-tokyo.ac.jp