SINGULAR LOCALLY SCALAR REPRESENTATIONS OF QUIVERS IN HILBERT SPACES AND SEPARATING FUNCTIONS

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Abstract

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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