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Singular locally scalar representations of quivers in Hilbert spaces and separating functions

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We consider locally scalar representations of extended Dynkin graphs in Hilbert spaces. The relation between these representations and the function ρ( n ) = 1 + ( n − 1 ) / ( n + 1 ) is established. We construct a family of separating functions that generalize the function ρ and play a similar role in a broader class of graphs.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 6, pp. 796–809, June, 2004.

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Redchuk, I.K., Roiter, A.V. Singular locally scalar representations of quivers in Hilbert spaces and separating functions. Ukr Math J 56, 947–963 (2004). https://doi.org/10.1007/PL00022183

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