Abstract
Associated with the q-deformation of the harmonic oscillator algebra we define an infinite dimensional braid group representation on the Hilbert space of the harmonic oscillator, and an extended Yang–Baxter system in the sense of Turaev. The corresponding link invariant is computed in some particular cases and coincides with the inverse of the Alexander–Conway polynomial. The R matrix of Uq(h4) can be interpreted as defining a baxterization of the intertwiners for semicyclic representations of SU(2)q at q=e2πi/N in the N→∞ limit. Finally we define new multicolored braid group representations and study their relation to the multivariable Alexander–Conway polynomial.
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