Topics in hidden symmetries. V

TL;DR

This paper explores the inverse problem of representation theory, emphasizing the diversity of representation methods and their surprising effects on abstract algebraic structures, offering new insights into the field.

Contribution

It provides a new perspective on the inverse problem of representation theory, highlighting the importance of representation diversity and its unexpected effects.

Findings

Representation diversity leads to intriguing effects

Richness of algebraic structures enhances the inverse problem

New insights into representation methods

Abstract

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.