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Nov 14, 2013 at 20:00 comment added André Henriques The short answer: I don't know. To cover the $n>1$ case, one would need to replace the Clifford by some other kind of algebra... and I have no idea what that could be. As far as (2) is concerned, I would say that it doesn't make sense to try to address (2) before understanding (1). So, I guess, I have nothing to offer, sorry.
Nov 14, 2013 at 19:40 history edited André Henriques CC BY-SA 3.0
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Nov 14, 2013 at 18:58 comment added Allen Knutson This looks pretty great, but I have two questions. (1) What about $n\rho$ for $n>1$? (2) Does this suggest that we should see the two strangely related spaces as living inside the same space ${\mathbb P}S$?
Nov 12, 2013 at 20:50 history answered André Henriques CC BY-SA 3.0