  We give a description of the centralizer algebras for tensor powers of spin
objects in the pre-modular categories $SO(N)_2$ (for $N$ odd) and $O(N)_2$ (for
$N$ even) in terms of quantum $(n-1)$-tori, via non-standard deformations of
$U\mathfrak{so}_N$. As a consequence we show that the corresponding braid group
representations are Gaussian representations, the images of which are finite
groups. This verifies special cases of a conjecture that braid group
representations coming from weakly integral braided fusion categories have
finite image.
