We generalize the definition of quiver representation to arbitrary reductive groups. The classical definition corresponds to the general linear group. We also show that for classical groups our definition gives symplectic and orthogonal representations of quivers with involution inverting the direction of arrows.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-2-1,
author = {Harm Derksen and Jerzy Weyman},
title = {Generalized quivers associated to reductive groups},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {151-173},
zbl = {1025.16010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-2-1}
}
Harm Derksen; Jerzy Weyman. Generalized quivers associated to reductive groups. Colloquium Mathematicae, Tome 91 (2002) pp. 151-173. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-2-1/