Some Invariant Theory and Representations of Quivers

Carol Chang
Northeastern University

Let $G$ be a reductive group acting linearly on the vector space
$V$. Let $S=k[V]$ be the regular functions on $V$ and $S^G$ be
the invariants in $S$ under the induced action of $G$ on $S$.  A
representation $V$ is called cofree if $S$ is a free $S^G$-module.

A classical problem in Invariant Theory is to determine for
which groups $G$ and spaces $V$ is $V$ a cofree representation.

In this talk, we discuss a new family of representations which are
cofree.  In particular,  given a finite quiver $Q$, we want to show
when the action of $SL(Q,d)$ on $Rep(Q,d)$ gives a cofree
representation.  We present a class of quivers which have this