  We define and study a lattice model which we argue is in the universality
class of the $OSp(2S+2|2S)$ supercoset sigma model for a large range of values
of the coupling constant $g_\sigma^2$. In this first paper, we analyze in
details the symmetries of this lattice model, in particular the decomposition
of the space of the quantum spin chain $V^{\otimes L}$ as a bimodule over
$OSp(2S+2|2S)$ and its commutant, the Brauer algebra $B_L(2)$. It turns out
that $V^{\otimes L}$ is a nonsemisimple module for both $OSp(2S+2|2S)$ and
$B_L(2)$. The results are used in the companion paper to elucidate the
structure of the (boundary) conformal field theory.
