Representations of Quivers with Free Modules of CovariantsCarol ChangNortheastern University
April 21,

ABSTRACT


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. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

