We present an algebraic approach to the description of bound states in the continuum (BICs) in finite systems with a discrete energy spectrum coupled to several decay channels. General estimations and bounds on the number of linearly independent BICs are derived. We show that the algebraic point of view provides straightforward and illustrative interpretations of typical well-known results, including the Friedrich–Wintgen mechanism and the Pavlov-Verevkin model. Pair-wise annihilation and repulsion of BICs in the energy–parameter space are discussed within generic two- and three-level models. An illustrative algebraic interpretation of such phenomena in Hilbert space is presented.

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