discussion with john huerta this evening...

i mentioned something about root diagram interpretation of cartan involution and maximla compact subgroup in special case of split real form... and vague idea of "extending cartan involution to irrep" or something like that... playing around with b2 case a bit, but then trying to imitate it somewhat in g2 case ... then trying to connect it with other stuff we think we sort of know about the g2 case ... including some stuff that we've been discussing recently coming form bor and montgomery ...

??something about ... root/weight diagram interpretation of "extending cartan involution to" (or something...) 7d irrep, and/or decomposing it wrt maximal compact subgroup... trying to relate this to what we've been (for some strange reason) calling "good vs evil" ... split octonions as some version of cayley-dickson construction from quaternions, or something ...

???also something about .... canonicalness (or something...) of product decomposition of maximal compact subgroup here ...

??something about trying to match up certain "dualities" here ... and so forth ....

??"good vs evil" ...

?? "fermion rolling on projective plane" (??something about how long root subalgebra relates to (??this?? ??or something???) projective plane ... and so forth...)

?? "rotation vs revolution" ... ???something about "heliocentric vs geocentric" and "interaction picture" (so to speak...) and "gauge-fixing" and so forth ... ???...

?? "space vs time" (analogies and/or relationship to split so(n) case, and so forth...)

?? "orientation vs point of contact" ...

???something about connecting "good vs evil" with both split octonion picture (via something about decomposing imaginary split octonions wrt maximal compact subgroup...???) and with rolling ball picture (via something about decomposing imaginary split octonions wrt maximal compact subgroup, which is something like so(3) X so(3), which we want to try to pretty directly relate to rolling ball... ??via ideas about "increase of homogeneousness" ??? ... and so forth ... ???), perhaps/hopefully helping to understand "tweak map" and so forth ...

??something about "tweak map" affecting evil coordinate in way depending on good coordinate or something ... good coordinate relating to projective plane and evil to fermion rolling on it ??? .... or something ... ???...