Homology representations of braid groups

R.J. Lawrence

Abstract: In this thesis, a topological construction of Hecke algebra representations associated with two-row Young diagrams is presented. These are the representations which appear in the one-variable Jones polynomial, looked at from the braid point of view. The construction used obtains these representations from monodromy representations on a vector bundle whole fibre is the homology of a complex manifold with a suitable, non-trivial, abelian locaal coefficient system. Alternatively, they are expressed as the monodromy representations obtained from the solutions of suitable systems of differential equations.

In the work of Tsuchiya & Kanie and Kohno, another construction of these representations can be found, in terms of the monodromy of n-point functions in conformal field theory. A comparison between the two constructions is made, which leads to a detailed correspondence, and the implications of this, in the context of conformal field theory, are very briefly discussed.

Keywords: Braid groups, Knot theory, Burau representation, Conformal Field Theory, Hecke algebra, representation theory, monodromy representation.

Length: 147 pages

Reference: D.Phil. Thesis, Univerity of Oxford (June 1989)

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Last updated on September 4th, 1996.