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Mar 27, 2022 at 18:27 vote accept asv
Mar 27, 2022 at 18:24 history edited Robert Bryant CC BY-SA 4.0
Modified my answer to take into account a conjugate representation of Spin(9,1) for which the identification does work.
Mar 27, 2022 at 14:47 history edited Robert Bryant CC BY-SA 4.0
Added an explicit identification of the 8-planes that belong to \Sigma.
Mar 27, 2022 at 13:13 comment added asv I think $H=Im(j)$. A proof is given below. Am I wrong? If I am correct your answer would be the final one.
Mar 27, 2022 at 11:57 history edited Robert Bryant CC BY-SA 4.0
Fixed another typos
Mar 27, 2022 at 11:26 history edited David Roberts CC BY-SA 4.0
fixed tex
Mar 27, 2022 at 10:14 history answered Robert Bryant CC BY-SA 4.0