  Let G denote either a special orthogonal group or a symplectic group defined
over the complex numbers. We prove the following saturation result for G: given
dominant weights \lambda^1, ..., \lambda^r such that the tensor product
V_{N\lambda^1} \otimes ... \otimes V_{N\lambda^r} contains nonzero G-invariants
for some N \ge 1, we show that the tensor product V_{2\lambda^1} \otimes ...
\otimes V_{2\lambda^r} also contains nonzero G-invariants. This extends results
of Kapovich-Millson and Belkale-Kumar and complements similar results for the
general linear group due to Knutson-Tao and Derksen-Weyman. Our techniques
involve the invariant theory of quivers equipped with an involution and the
generic representation theory of certain quivers with relations.
