The Corepresentations of Continuous Groups

TL;DR

This paper develops a corepresentation theory for continuous groups that does not assume the subgroup with antilinear operations is unitary, providing a foundation that can derive formulas for unitary groups.

Contribution

It introduces a generalized corepresentation framework for continuous groups without the unitarity assumption, extending existing theories.

Findings

Formulas for corepresentations with unitary groups can be derived from the new framework.

The theory broadens the understanding of group corepresentations beyond the unitarity constraint.

Provides a basis for further exploration of non-unitary subgroup corepresentations.

Abstract

The corepresentation theory of continuous groups is presented without the assumption that the subgroup $G$ of the group with antilinear operations is unitary. The formulas of the corepresentation theory with unitary groups $G$ can be obtained from this presentation.