  We examine a quantum group extension of the standard model with the symmetry
$SU(3) \times SU(2) \times U(1)\times $ global $SLq(2)$. The quantum fields of
this extended model lie in the state space of the $SLq(2)$ algebra. The normal
modes or field quanta carry the factors $D^j_{mm^\prime} (q|abcd)$, which are
irreducible representations of $SLq(2)$ (which is also the knot algebra). We
describe these field quanta as quantum knots and set $(j,m,m^\prime)= 1/2 (N,w,
\pm r+1)$ where the $(N,w,r)$ are restricted to be (the number of crossings,
the writhe, the rotation) respectively, of a classical knot.
  There is an empirical one-to-one correspondence between the four quantum
trefoils and the four families of elementary fermions, a correspondence that
may be expressed as $(j,m,m^\prime)=3(t,-t_3, -t_0)$, where the four quantum
trefoils are labelled by $(j,m,m^\prime)$ and where the four families are
labelled in the standard model by the isotopic and hypercharge indices
$(t,t_3,-t_0)$. We propose extending this correlation to all representations by
attaching $D_{-3t-3t_0}^{3t} (q| abcd) $ to the field operator of every
particle labelled by $(t,t_3, t_0)$ in the standard model. Then the elementary
fermions $(t=1/2)$ belong to the $j=3/2$ representation of $SLq(2)$. The
elements of the fundamental representation $j=1/2$ will be called preons and
$D_{-3t,-3t_o}^{3t}$ may be interpreted as describing the creation operator of
a composite particle composed of elementary preons. $D_{m m^\prime}^j$ also may
be interpreted to describe a quantum knot when expressed as $D_{\frac w2
\frac{\pm r+1}2} ^{N/2}$ These complementary descriptions may be understood as
describing a composite particle of $N$ preons bound by a knotted boson field
with $N$ crossings.
