Combinatorics and Algebraic Topology of Configurations

# Conformal blocks and homological representations of braid groups - "Combinatorics and Algebraic Topology of Configurations" (Workshop 2015)

speaker: Toshitake Kohno (Graduate School of Mathematical Sciences, the University of Tokyo)

abstract: We show that specializations of the homological representationsof braid groups are equivalent to the monodromy of the KZ equation with values in the space of null vectors in the tensor product of Verma modules when the parameters are generic. Here the representations of the solutions of the KZ equation by hypergeometric integrals due to Schechtman, Varchenko and others play an important role. By this construction we recover quantum symmetry of the monodromy of KZ connection due to Drinfel'd and myself by means of the action of the quantum groups on twisted cycles. In the case of special parameters corresponding to conformal field theory, we give a description of twisted cycles.

timetable:
Tue 17 Feb, 9:30 - 10:10, Aula Dini
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