?? "generalized pluecker relations" (jargon term for this ?? ...) for g2 ... ?? presented in various hopefully nice conceptual ways .... octonion-ish ... rolling-ball-ish .... ?? use of long root subalgebra ??

1d isotropic subalgs of imaginary split octonions ....

7 basic imaginary octonions ...

?? confusion about whether i should think in terms of these or ["coefficients of" them] =?= dual basis vectors ... even though sort of doesn't matter in this case .... ????....

2d ....

?? start with grassmanian "7 choose 2" ... ??? which is 21-dimensional ...

?? then add isotropy constraint ????? .....

??? generalized pluecker relations for 2 vanilla end dots of so(7) ... 1d and 2d isotropics ??? plus extra relations saying that the 2d ones are isotropic in the stronger sense ... octonionic ...

?? well let's see ... as far as the duality confusion here, i mean ... should be able to straighten it out .... ?? anti-tautological line bundle has sections ... ???

?? 21-dimensional irrep of so(7) .... ?? adjoint irrep in fact ?? ... with ?-dim grassmanian in its 20-dim projective space ... ???..... 14-dim adjoint rep of g2 inside 21-dim .... 5-dim grassmanian inside that .... ???? the 13-dim and the ?-dim inside the 20-dim intersect "higher-dimensionally than expected" ??? ...