  The standard quantum states of $n$ complex Grassmann variables with a
free-particle Lagrangian transform as a spinor of SO(2n). However, the same
`free-fermion' model has a non-linearly realized $SU(n|1)$ symmetry; it can be
viewed as the mechanics of a `particle' on the Grassmann-odd coset space
$SU(n|1)/U(n)$. We implement a quantization of this model for which the states
with non-zero norm transform as a representation of $SU(n|1)$, the
representation depending on the U(1) charge of the wave-function. For $n=2$ the
wave-function can be interpreted as a BRST superfield.
