  The symplectic blob algebras are a family of finite dimensional
noncommutative algebras over $\mathbb{Z}[X_1,X_2,X_3,X_4,X_5,X_6]$ that can be
defined in terms of planar diagrams in a way that extends the Temperley-Lieb
and (ordinary) blob algebras.
  In this paper we construct a new "tensor space" representation of the
symplectic blob algebra $\mathcal{A} \otimes \sba$ for each $n \in \mathbb{N}$,
for $\mathcal{A}$ a particular commutative ring with indeterminates. The form
of this representation is motivated by the XXZ representation of the
Temperley-Lieb algebra $\TL_n$ \cite{jimbo86} and the related Martin-Woodcock
representation of the blob algebra $b_n$ \cite{martinwoodcock2003}. For $k$ an
algebraically closed field, and for any
$(\delta,\delta_L,\delta_R,\kappa_L,\kappa_R,\kappa) \in k^{6}$, the algebra
$\sba$ specialises to a $k$-algebra
$\sba(\delta,\delta_L,\delta_R,\kappa_L,\kappa_R,\kappa)$. For any such
specialisation, our representation passes to a
$\sba(\delta,\delta_L,\delta_R,\kappa_L,\kappa_R,\kappa)$-module
$\mathcal{V}(n)$.
