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    Braid groups and symmetric groups

    Bigelow, Stephen
    ( Click here for pdf version )

    Representations of the symmetric group are not well understood when the field has non-zero characteristic. They are closely related to representations of the Hecke algebra when the parameter q is a root of unity. Lawrence has shown how these representations can be defined topologically, as an action of the braid group on the homology of certain configuration spaces. I will use some examples to illustrate how this enables one to ``see'' why representations become reducible at some roots of unity.