  The $D=11$ pure spinor formulation of the superparticle allows a simple
realization of covariant quantization, unlike the $D=11$ Brink-Schwarz-like
superparticle. We explicitly show the equivalence between the cohomologies of
these two models in the context of two different group decompositions:
$SO(10,1) \rightarrow SO(1,1)\times SO(9)$ and $SO(10,1) \rightarrow
SO(3,1)\times SO(7)$. We also carry out a light-cone analysis of the pure
spinor cohomology, and show that it correctly reproduces the $SO(9)$ equations
of motion for $D=11$ linearized supergravity.
