?? g acts homogeneously on g/b, of course .... and t maps to g ..... ?????? orbit decomposition of g/b wrt t ???? ...... (g,t)-double cosets .... ?? flag-apartment orientations ... ??? but which one to pick ?????.......
?? maybe does seem somewhat promising though ?? ... ?? "all the flags whose orientation towards the standard apartment is ..." .... ??? ....
??? orientation towards standard apartment .... giving orientations towards parts of standard apartment ... ??? .... ??? .... logic ... disjunction, conjunction .... ???? ....
?? also ... _of_ parts, towards parts ... ???? .....
?? irreducibility of toric variety ?? .... disjunction vs conjunction ... ??? ....
?? blow-downs ... ?? same torus, so still orientations towards the standard apartment ... ?? but now you only look at part of the flag ...
?? some orbit closure of t -> g -> perm(g/h) with h general parabolic now instead of borel ???
?? flag-apartment orientations ... ?? classification of flag triples and/or flag [n+1]-tuples ... ??? .... ?? showing up in .... ?? hecke algebras and/or cohomology algebras of flag varieties ... ??? .... multiplication operations therein ... ???....
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