Topics in hidden symmetries. V

This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the concrete ones as well as on the abstract objects themselves. The results of researches allow to state that the actual richness and attractiveness of the inverse problem of representation theory are based not only on a large scope of various interesting abstract algebraic structures, which may be concretely represented and somehow unravelled, but also on the diversity of the manners of representation, which may produce very intriguing unexpected and nontrivial effects under the intent look even in the simple and almost hackneyed situations.