Invariants of quivers under the action of classical groups

Details Invariants of quivers under the action of classical groups Invariants of quivers under the action of classical groups

2006-08-30

arxiv.org/abs/math/0608750v2

J. Algebra 321 (2009), 1079-1106.

Mathematics

Representation Theory

41 pages; v2. minor corrections

Scientific paper

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 uses the reduction to semi-invariants of mixed representations of a quiver and the decomposition formula that generalizes Amitsur's formula for the determinant.

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