Invariants of quivers under the action of classical groups

JOURNAL OF ALGEBRA

卷:321

Article

Lopatin, A. A.¹ 

[1] Russian Acad Sci, Inst Math, Siberian Branch, Omsk 644099, Russia

关键词: Representations of quivers;    Invariants;    Classical linear groups;    Good filtration;    Pfaffian;   

DOI  :  10.1016/j.jalgebra.2008.11.018

来源: Elsevier

【 摘 要 】

We consider a generalization or representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical linear 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, semi-invariants of supermixed representations of quivers are established. As a consequence, 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 and the decomposition formula that generalizes Amitsur's formula for the determinant. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free