Get-together Math Seminar

Speaker: Toshitake Kohno (U. Tokyo)
Title: Quantum symmetry in homological representations of braid groups
Date (JST): Thu, Nov 22, 2012, 15:30 - 17:00
Place: Seminar Room A
Abstract: Homological representations of braid groups are defined as the action of homeomorphisms of a punctured disk on the homology of an abelian covering of its configuration space. These representations were extensively studied by Lawrence, Krammer and Bigelow. In this talk we show that specializations of the homological representations of 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. To prove this we use representations of the solutions of the KZ equation by hypergeometric integrals due to Schechtman, Varchenko and others. We describe the action of quantum groups on the space of homology with local coefficients and recover quantum symmetry in homological representations.