  Let G be a complex reductive group acting on a finite-dimensional complex
vector space H. Let B be a Borel subgroup of G and let T be the associated
torus. The Mumford cone is the polyhedral cone generated by the T-weights of
the polynomial functions on H which are semi-invariant under the Borel
subgroup. In this article, we determine the inequalities of the Mumford cone in
the case of the linear representation associated to a quiver and a dimension
vector n=(n_x). We give these inequalities in terms of filtered dimension
vectors, and we directly adapt Schofield's argument to inductively determine
the dimension vectors of general subrepresentations in the filtered context. In
particular, this gives one further proof of the Horn inequalities for tensor
products.
