Tuesday, August 17, 2010

??so... ??we should try to develop some nice ways of understanding the relationship between the symmetric monoidal category of representations of the simple lie group (or something like that) and the one of coherent sheaves over the flag variety (as well as some other related ones...) by means of... certain diagrammatic techniques involving the root system...which i'm vaguely imagining at the moment but too vaguely to articulate very clearly right now... of course we've thought about things sort of like this before, but... i think that i have certain ideas now about things to try here... for example about thinking of general partial flags as something sort of like "superpositions" (or something like that...) of the ones in the favorite apartment...
??...

one more ingredient to try to incorporate into the picture is the way in which the poisson algebra of the coadjoint orbit occurs as the scaling limit of... something or other... ??...

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