  The character of holomorphic functions on the space of pure spinors in ten,
eleven and twelve dimensions is calculated. From this character formula, we
derive in a manifestly covariant way various central charges which appear in
the pure spinor formalism for the superstring. We also derive in a simple way
the zero momentum cohomology of the pure spinor BRST operator for the D=10 and
D=11 superparticle.
