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Notes on spinors in low dimension
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The purpose of these old notes (written in 1998 during a research project on holonomy of pseudo-Riemannian manifolds of type (10,1)) is to determine the orbit structure of the groups Spin(p,q) acting on their spinor spaces for the values (p,q) = (8,0), (9,0), (9,1), (10,0), (10,1), and (10,2). I'm making them available on the arXiv because I continue to get requests for them as well as questions about how they can be cited.
Forward citations
Cited by 2 Pith papers
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Standard Model Symmetries and the Nested Embeddings of $\mathbb{R}\subset\mathbb{C}\subset\mathbb{H}\subset\mathbb{O}$
The Standard Model gauge group and its charge operators emerge from O⊕H⊕C⊕R by stabilizing top-graded elements and imposing an equal-trace condition.
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Explicit Families of Spinor Representations
A complete explicit family of real spinor representations is assembled from tensor products of low-dimensional quaternionic, complex, and real modules.
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