  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.
