  We consider the gauged free fermionic matrix model, for a single fermionic
matrix. In the large $N$ limit this system describes a $c=1/2$ chiral fermion
in $1+1$ dimensions. The Gauss' law constraint implies that to obtain a
physical state, indices of the fermionic matrices must be fully contracted, to
form a singlet. There are two ways in which this can be achieved: one can
consider a trace basis formed from products of traces of fermionic matrices or
one can consider a Schur function basis, labeled by Young diagrams. The Schur
polynomials for the fermions involve a twisted character, as a consequence of
Fermi statistics. The main result of this paper is a proof that the trace and
Schur bases coincide up to a simple normalization coefficient that we have
computed.
