**Topological approach to the Iwahori-Hecke algebra**

**R.J. Lawrence**

**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. A***5** (1990) 3213-3219.
MR1062959 (91j:32043) (review by * Toshitake Kohno *.)

*Last updated on September 4th, 1996.*

ruthel@ma.huji.ac.il