**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.*

ruthel@ma.huji.ac.il