We study indecomposable representations of quivers on separable infinite-dimensional Hilbert spaces by bounded operators. We exhibit several concrete examples and investigate duality theorem between reflection functors. We also show a complement of Gabriel's theorem. Let Γ be a finite, connected quiver. If its underlying undirected graph contains one of extended Dynkin diagrams over(A, ̃)n(n ≥ 0), over(D, ̃)n(n ≥ 4), over(E, ̃)6, over(E, ̃)7 and over(E, ̃)8, then there exists an indecomposable representation of Γ on separable infinite-dimensional Hilbert spaces.
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