Fundaments of Quaternionic Clifford Analysis I

TL;DR

This paper develops the foundational aspects of quaternionic Clifford analysis by exploring the quaternionic structure on Euclidean space and examining invariance under symplectic group actions.

Contribution

It introduces a quaternionic structure on Euclidean space and studies the fundamental principles of quaternionic and symplectic Clifford analysis with respect to symplectic invariance.

Findings

Established quaternionic structure on Euclidean space

Analyzed invariance under symplectic group actions

Developed foundational concepts for quaternionic Clifford analysis

Abstract

Introducing a quaternionic structure on Euclidean space, the fundaments for quaternionic and symplectic Clifford analysis are studied in detail from the viewpoint of invariance for the symplectic group action.