Lectures on Representations of Quivers by William Crawley-Boevey ...

§10. Further topics
In this section I want to list some of the topics which have attracted
interest in the past, and which are areas of present research. The lists of
papers are only meant to be pointers: you should consult the references in
the listed papers for more information.
(1) Kac’s Theorem: for any quiver the dimension vectors of the
indecomposables are the positive roots of the graph.
V.Kac, Infinite root systems, representations of graphs and invariant
theory I,II, Invent. Math 56 (1980), 57-92, J. Algebra 77 (1982),
141-162.
V.Kac, Root systems, representations of quivers and invariant theory, in
Springer Lec. Notes 996 (1983), 74-108.
H.Kraft & Ch.Riedtmann, Geometry of representations of quivers, in
Representations of algebras (ed. P.Webb) London Math. Soc. Lec. Note
Series 116 (1986), 109-145.
(2) Invariant theory and geometry for the action of the group GL(¤ ) on the
variety Rep(¤ ).
C.Procesi, The invariant theory of n£ n matrices, Adv. Math. 19(1976),
306-381.
C.M.Ringel, The rational invariants of the tame quivers, Invent. Math.,
58(1980), 217-239.
L.Le Bruyn & C.Procesi, Semisimple representations of quivers, Trans. Amer.
Math. Soc. 317 (1990), 585-598.
Ch.Riedtmann & A.Schofield, On open orbits and their complements, J.Algebra
130 (1990), 388-411.
A.Schofield, Semi-invariants of quivers, J. London Math. Soc. 43 (1991),
385-395.
A.Schofield, Generic representations of quivers, preprint.
(3) Construction of the Lie algebra and quantum group of type from the
representations of a quiver with graph .
C.M.Ringel, Hall polynomials for the representation-finite hereditary
algebras, Adv. Math. 84 (1990), 137-178.
C.M.Ringel, Hall algebras and quantum groups, Invent. Math. 101 (1990),
583-592.
G.Lusztig, Quivers, perverse sheaves, and quantized enveloping algebras, J.
Amer. Math. Soc. 4 (1991), 365-421.
A.Schofield, Quivers and Kac-Moody Lie algebras, preprint.
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