A ug 2 00 6 Invariants of quivers under the action of classical groups . A . A

Invariants of quivers under the action of classical groups. Abstract We consider a generalization of representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical groups, instead of a product of the general linear groups, and by considering the dual action of groups on " vertex " vector spaces together with the usual action. A generating system for the corresponding algebra of invariants is found. In particular, a generating system for the algebra of SO(n)-invariants of several matrices is constructed over a field of characteristic different from 2. The proof is based on the reduction to semi-invariants of mixed representations of a quiver and on the decomposition formula, which generalizes Amitsur's formula for the determinant.