Topological approach to the Iwahori-Hecke algebra
Abstract: In this paper a topological construction of representations of the A_n^(1)-series of Hecke algebras, associated with 2-row Young diagrams, will be announced. This construction gives the representation in terms of the monodromy representation obtained from a vector bundle over the configuration space of n 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 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 P^1 is used to produce a braid group representation which factors through the Hecke algebra.
Keywords: braid group, Hecke algebra, monodromy representation, Gauss-Manin connection, configuration space, local coefficient system
AMS subject classification: 32S40 14F40 20F36 57M25 81T40
Length: 7 pages
Reference: Int. J. Mod. Phys. A5 (1990) 3213-3219. MR1062959 (91j:32043) (review by Toshitake Kohno .)
Last updated on September 4th, 1996.