Geodesic
Orthoscalar quiver representations corresponding to extended Dynkin graphs in the category of Hilbert spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 2, pp. 57-73

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It is known that finitely representable quivers correspond to Dynkin graphs and tame quivers correspond to extended Dynkin graphs. In an earlier paper, the authors generalized some of these results to locally scalar (later renamed to orthoscalar) quiver representations in Hilbert spaces; in particular, an analog of the Gabriel theorem was proved. In this paper, we study the relationships between indecomposable representations in the category of orthoscalar representations and indecomposable representations in the category of all quiver representations. For the quivers corresponding to extended Dynkin graphs, the indecomposable orthoscalar representations are classified up to unitary equivalence.
Keywords: quiver, orthoscalar representation, Hilbert space, extended Dynkin graphs, unitary equivalence. 
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     author = {S. A. Kruglyak and L. A. Nazarova and A. V. Roiter},
     title = {Orthoscalar quiver representations corresponding to extended {Dynkin} graphs in the category of {Hilbert} spaces},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2010_44_2_a5/}
}
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S. A. Kruglyak; L. A. Nazarova; A. V. Roiter. Orthoscalar quiver representations corresponding to extended Dynkin graphs in the category of Hilbert spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 2, pp. 57-73. http://geodesic.mathdoc.fr/item/FAA_2010_44_2_a5/