A quiver is a directed graph specified by a set of vertices, a set of arrows, and source and target maps from arrows to vertices.
Loops and multiple arrows with the same endpoints are allowed. A representation assigns
a vector space to each vertex and a linear map to
each arrow. For example, a quiver with one vertex and one loop is represented by
a vector space with one endomorphism.
Framed quivers additionally assign spaces at vertices and maps between the vertex spaces and framing
spaces. Their cotangent representation spaces and moment maps define Nakajima
quiver varieties.
Etingof, P.; Golberg, O.; Hensel, S.; Liu, T.; Schwendner, A.; Vaintrob, D.; and Yudovina, E. Introduction to Representation Theory.
Providence, RI: Amer. Math. Soc., 2011. https://doi.org/10.1090/stml/059.Ginzburg,
V. "Lectures on Nakajima's Quiver Varieties." In Geometric Methods in
Representation Theory, I (Ed. M. Brion). Paris, France: Soc. Math. France,
pp. 145-219, 2012. https://smf.emath.fr/publications/notes-sur-les-varietes-de-carquois-de-nakajima.
at vertices and maps between the vertex spaces and framing
spaces. Their cotangent representation spaces and moment maps define Nakajima
quiver varieties.
