Communications in Mathematical Physics

, Volume 135, Issue 1, pp 141–191 | Cite as

Homological representations of the Hecke algebra

  • R. J. Lawrence


In this paper a topological construction of representations of theA 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 ofn-point functions in a conformal field theory onP1. 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].


Neural Network Field Theory Complex System Nonlinear Dynamics Vector Bundle 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • R. J. Lawrence
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

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