A topological approach to representations of the Iwahori-Hecke algebra

In this paper a topological construction of representations of the -series of Hecke algebras, associated with 2-row Young diagrams, will be announced. This construction gives the representations in terms of the monodromy representation obtained from a vector bundle over the configuration space of η points in the complex plane. The fibres are homology spaces of configuration spaces of points in a punctured complex plane, with a suitable twisted local coefficient system, and there is thus a natural flat connection on the vector bundle. It is also shown that there is a close correspondence between this construction and the work of Tsuchiya and Kanie, in which the monodromy of n-point functions for a conformal field theory on P1 is used to produce a braid group representation which factors through the Hecke algebra.