Abstract
The character of holomorphic functions on the space of pure spinors in 10, 11 and 12 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
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