  As shown by P-E Paradan, the set of orbits contained in the sum of two
holomorphic orbits in the Lie algebra of U(p,q) is determined by a set of
inequalities similar to the Horn inequalities for the sum of conjugacy classes
of two Hermitian matrices. We give another proof of these inequalities using
representations of quivers. We also discuss the implications of these
inequalities for the decomposition of tensor products of representations of the
holomorphic discrete series.
