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Communications in Mathematical Physics

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

Homological representations of the Hecke algebra

  • R. J. Lawrence
Article

Abstract

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].

Keywords

Neural Network Field Theory Complex System Nonlinear Dynamics Vector Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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