Sinle-valued and spinor representations of orientation-preserved four-dimensional cubic group

TL;DR

This paper computes the single-valued and spinor representations of the orientation-preserved four-dimensional cubic group, expanding understanding of its structure based on prior work on the four-dimensional cubic group.

Contribution

It provides explicit calculations of representations of the four-dimensional cubic group and its orientation-preserved subgroup, a novel extension of previous research.

Findings

Explicit representations of $SO_4$ derived

Enhanced understanding of four-dimensional cubic symmetry

Foundation for further mathematical or physical applications

Abstract

We calculate the single-valued and spinor representations of $SO_4$, the orientation-preserved subgroup of $O_4$, on the base of our previous work on four-dimensional cubic group $O_4$.