Greg Egan on Nostr: n=9 is the first value when n^2 (the dimension of GL(n,C)) is greater than ...

n=9 is the first value when n^2 (the dimension of GL(n,C)) is greater than Binomial(n,3) (the dimension of the space of trivectors).

But 9^2 = 81 and Binomial(8,3) = 84, so naively I would have thought the space of orbits would be 3-dimensional, not 4-dimensional. I guess the action of GL(9,C) on the trivectors must produce 80-dimensional orbits rather than 81-dimensional.