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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

property.