Response to the Comment by G. Emch on Projective Group Representations in Quaternionic Hilbert Space

TL;DR

This paper clarifies different definitions of quaternionic projective group representations, introduces a more inclusive weak definition, and develops a comprehensive theory accommodating both quaternionic and complex cases.

Contribution

It proposes a new weak definition of quaternionic projective representations that includes complex embeddings, expanding the theoretical framework.

Findings

Weak definition encompasses complex embeddings

Develops a detailed theory for quaternionic and complex representations

Clarifies limitations of previous strong definitions

Abstract

We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embeddings, and leads to a detailed theory of quaternionic, as well as complex, projective group representations.