  Let Det_n denote the closure of the GL_{n^2}(C)-orbit of the determinant
polynomial det_n with respect to linear substitution. The highest weights
(partitions) of irreducible GL_{n^2}(C)-representations occurring in the
coordinate ring of Det_n form a finitely generated monoid S(Det_n). We prove
that the saturation of S(Det_n) contains all partitions lambda with length at
most n and size divisible by n. This implies that representation theoretic
obstructions for the permanent versus determinant problem must be holes of the
monoid S(Det_n).
