Some remarks on representations of quivers and infinite root systems

  • Victor G. Kač
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 832)


Vector Space Versus Dynkin Diagram Cartan Matrix Linear Algebraic Group Base Field 
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  1. [1]
    DLAB, V., RINGEL, C.M.: Indecomposable representations of graphs and algebras. Memoirs of Amer. Math. Soc. 6, 173, 1–57 (1976).MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    GABRIEL, P.: Indecomposable representations II. Symposia Math. Inst. Naz. Alta Mat. XI, 81–104 (1973).MathSciNetzbMATHGoogle Scholar
  3. [3]
    KAC, V.G.: Infinite dimensional algebras, Dedekind’s η-function, classical Möbius function and the very strange formula. Adv. in Math. 30, 85–136 (1978).MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    KAC, V.G.: Infinite root systems, representations of graphs and invariant theory. Inv. Math. 56(1980), 57–92MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    OVSIENKO, S.A.: On the root systems for arbitrary graphs, Matrix Problems, 81–87 (1977).Google Scholar
  6. [6]
    RINGEL, C.M.: Reflection functors for hereditary algebras, preprint (1979).Google Scholar
  7. [7]
    SATO, M., KIMURA, T.: A classification of irreducible prehomogeneous vector spaces and their relative invariants. Nagoya Math. J. 65, 1–155 (1977).MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    SERRE, J.-P.: Algèbres de Lie semi-simples complexes, New York-Amsterdam: Benjamin 1966.zbMATHGoogle Scholar
  9. [9]
    DELIGNE, P.: La conjecture de Weil II, Publ. Math. IHES, to appear.Google Scholar
  10. [10]
    KOECHER, M.: Positivitätsbereiche im Rn, Amer. J. Math. 79, 3, 575–596 (1957).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Victor G. Kač
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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