  We define a family of representations $\{\rho_n\}_{n\geq 0}$ of a pure braid
group $P_{2k}$. These representations are obtained from an action of $P_{2k}$
on a certain type of $A_2$ web space with color $n$. The $A_2$ web space is a
generalization of the Kauffman bracket skein module of a disk with marked
points on its boundary. We also introduce a triangle-free basis of such an
$A_2$ web space and calculate matrix representations of $\rho_n$ about the
standard generators of $P_{2k}$.
