  This is the third in a series of papers on standard monomial theory and
invariant theory of arc spaces. For any algebraically closed field $K$, we
prove the arc space analogue of the first and second fundamental theorems of
invariant theory for the special linear group. This is more subtle than the
results for the general linear and symplectic groups obtained in the first two
papers because the arc space of the corresponding affine quotients can be
nonreduced.
