Representations of Quivers with Free Modules of Covariants

Carol Chang

Northeastern University

April 21,
refreshments at 3:45pm


A quiver is an oriented graph Q=(Q_0,Q_1) where Q_0 is the set of vertices and Q_1 is the set of arrows. For an arrow a in Q_1, a: tail(a) -> head(a). A representation V of a quiver Q is a collection of vector spaces at each vertex, together with linear maps corresponding to each arrow. Specifiying a dimension at each vertex of the quiver, a representation is then determined by specifying the linear maps., or in other words by a point in a certain affine space, Rep(Q,d).

Given a finite connected quiver Q, we are interested in when the action of SL(Q,d) on Rep(Q,d) gives a cofree representation. In particular, we are interested in studying the situation when the modules of covariants are free k[Rep(Q,d)]^{SL(Q,d)}-modules. We will discuss when quivers have free modules of covariants.

Speaker's Contact Info: cchang(at-sign)

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