?? unification between :

1 grinding out construction of given irrep of simple (?? ...) alg gp (?? ...) via "schur functor" .... ???? ..... ???? .... ag doctrine .... ???? ....

2 constructing that irrep as holomorphic (?? ...) sections of hopefully somewhat evident line bundle over flag variety .... ??? .... taking very conceptually slick "algebraic" approach to "holomorphic section" here .... ????? ......

?? example ....

??irrep of gl(2) .... functor assigning to 2d vsp v new vsp v' , obtained by ... ???.... p(v) as (more or less ...) dimensional theory ... certain line object in that theory ..... ???? .... sections thereof ..... ????? .... ??? ....


?? idea that "getting hold of not-quite-irrep instead of irrep is sometimes almost as good" (?? ...) vs ... ?? idea that it's too vacuous, because for example "cayley rep contains everything so you could just declare victory and quit right there" ... ...??? so, first idea here needs some refinement ... ?? getting hold of irrep, up to it being "categorified leading term" in non-irrep ... ??? various ways of trying to formalize "leading" here .... ???? ....

?? applying schur fr to cayley rep of ... ??? finite gp ??? ... other sort of gp ??? .... ???? ....

?? hmm, maybe the unification above is really just that of "holomorphic sections of line bundle over flag variety" idea with "grade (?? wrt "highest weight" grading rather than wrt "weight" grading ?? ...) of multihomogeneous coordinate algebra of flag variety" idea ..... ??? .... ?? not sure how close to thinking this outloud we've come before .... ??? ...

??? bott ... ?? riemann-roch .... ???? .....