??so what about maximal compact subgroup of so(2,3) ?? ... as so(2) X so(3) ... or something ... ???which numerologically seems to fit with the "anti-symmetrization wrt antipode involution of root diagram" (or something...)... ??but can we see it in more detail??...

???something about "extent to which cartan involution extends to reps" .... ???or something, and so forth ???? something about so(2,3) case, and so forth ... ???also something about g2 case for huerta??...

??something about ... ??adjoint rep of so(n) as exterior square of tautological rep ... using this to connect root diagram with "matrix picture" ... ??something about connecting this with some stuff that we maybe worked out about the matrix picture around the time that we were looking at the numerology of classifying invariant distributions on flag manifolds, and so forth ...

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??something about "antisymmetrized" and "symmetrized" part of 5d rep as giving respectively 2d and 3d reps of maximal compact obtained as "antisymmetrized" part of adjoint rep ??? .... ???or something??? ??and so forth ?? ... ??but how does this relate to, for example, the "bottom row" of the adjoint rep as "flat 2+1 spacetime" ?? ... and so forth ... ???...