 
Summary: CLASSIFYING REPRESENTATIONS BY WAY OF GRASSMANNIANS
Birge HuisgenZimmermann
Dedicated to the memory of Sheila Brenner
Abstract. Let be a finite dimensional algebra over an algebraically closed field. Criteria
are given which characterize existence of a fine or coarse moduli space classifying, up to
isomorphism, the representations of with fixed dimension d and fixed squarefree top T. Next
to providing a complete theoretical picture, some of these equivalent conditions are readily
checkable from quiver and relations. In case of existence of a moduli space unexpectedly
frequent in light of the stringency of fine classification this space is always projective and,
in fact, arises as a closed subvariety GrassT
d of a classical Grassmannian. Even when the full
moduli problem fails to be solvable, the variety GrassT
d is seen to have distinctive properties
recommending it as a substitute for a moduli space. As an application, a characterization
of the algebras having only finitely many representations with fixed simple top is obtained;
in this case of `finite local representation type at a given simple T', the radical layering`
JlM/Jl+1M
´
l0
is shown to be a classifying invariant for the modules with top T. This
