Abstract

Let Q be a quiver without oriented cycles. For a dimension vector Beta let Rep(Q,Beta) be the set of representations of Q with dimension vector Beta. The group GL(Q, Beta) acts on Rep(Q,Beta). In this paper we show that the ring of semi-invariants SI(Q,Beta) is spanned by special semi-invariants c^V associated to representations V of Q. From this we show that the set of weights appearing in SI(Q,Beta) is saturated.