  The $q$--deformation $U_q (h_4)$ of the harmonic oscillator algebra is
defined and proved to be a Ribbon Hopf algebra.Associated with this Hopf
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 $U_q (h_4)$ can be interpreted as defining a
baxterization of the intertwiners for semicyclic representations of $SU(2)_q$
at $q=e^{2 \pi i/N}$ in the $N \rightarrow \infty$ limit.Finally we define new
multicolored braid group representations and study their relation to the
multivariable Alexander--Conway polynomial.
