Homological representations of the 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 given. This construction gives the representations in terms of the monodromy representation obtained from a vector bundle on which there is a natural flat connection. The fibres of the vector bundle are homology spaces of configuration spaces of points in C, with a suitable twisted local coefficient system. It is also shown that there is a close correspondence between this construction and the work of Tsuchiya and Kanie, who constructed Hecke algebra representations from the monodromy of n-point functions in a conformal field theory on P 1. This work has significance in relation to the one-variable Jones polynomial, which can be expressed in terms of characters of the Iwahori-Hecke algebras associated with 2-row Young diagrams; it gives rise to a topological description of the Jones polynomial, which will be discussed elsewhere [L2].
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- December 1990
- DOI:
- 10.1007/BF02097660
- Bibcode:
- 1990CMaPh.135..141L