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• W2047444328 abstract "We show how the Conway Alexander polynomial arises from theq deformation of (Z 2 graded)sl(n, n) algebras. In the simplestsl(1, 1) case we then establish connection between classical knot theory and its modern versions based on quantum groups. We first shown how the crystal and the fundamental group of the complement of a knot give rise naturally to the Burau representation of the braid group. The Burau matrix is then transformed into theU q sl(1, 1) R matrix by going to the exterior power algebra. Using a det=str identity, this allows us to recover the state model of [K2, 89] as well. We also show how theU q> sl(1, 1) algebra describes free fermions “propagating” on the knot diagram. We rewrite the Conway Alexander polynomial as a Berezin integral, and thus as an apparently new determinant." @default.
• W2047444328 created "2016-06-24" @default.
• W2047444328 creator A5027386297 @default.
• W2047444328 creator A5057018104 @default.
• W2047444328 date "1991-10-01" @default.
• W2047444328 modified "2023-10-18" @default.
• W2047444328 title "Free fermions and the Alexander-Conway polynomial" @default.
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• W2047444328 doi "https://doi.org/10.1007/bf02101508" @default.
• W2047444328 hasPublicationYear "1991" @default.
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