TL;DR
This paper explores the structure of a 32-dimensional representation space related to Spin(9,1) and SL(2,R), using twistor geometry to interpret an open orbit as an analogue of invertible octonionic matrices.
Contribution
It introduces a novel geometric interpretation of octonionic matrix analogues through the study of homogeneous subspaces in a high-dimensional representation space.
Findings
Identification of an open orbit as a substitute for invertible octonionic matrices
Analysis of natural homogeneous subspaces in the representation space
Application of twistor geometry in eight dimensions
Abstract
We interpret an open orbit in a 32-dimensional representation space of Spin(9,1) x SL(2,R) as a substitute for the non-existent group of invertible 2x2 matrices over the octonions and study various natural homogeneous subspaces. The approach is via twistor geometry in eight dimensions.
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