Wednesday, November 24, 2010

notes for next meeting with alex

??possible relationship between kaleidoscope mirror reflection associated with particular dot d in dynkin diagram, and "flipping the direction of all the arrows touching d" or something... ??possible "pull/push" ideas here?? ... underlying/free ... ??? or something??...

??guess about isomorphisms between underlying dynkin diagrams of dynkin quivers, and problems with it... ??...

??stuff about various concepts of "cartan matrix" (??as discussed by benson for example??... ???something about "euler form" or something like that??) and relationships between them and de/categorification ideas, and quiver representations, and basis (??or something??) of irreducibles vs basis of indecomposable projectives, and "projective cover" (or something) and so forth...

(what were those buzzwords (?buzznames?) associated with basis of irreducibles vs basis of indecomposable projectives (??or something?? ... and so forth...) in "category o"?? ... there's "bgg resolution" and "jantzen filtration" and so forth, but isn't there some other buzzname or buzznames that i'm thinking of?? ... hmm, i think that i'm thinking of some kind of "reciprocity", but what _was_ the buzzname attached to it?? ??maybe "bgg reciprocity" or something like that?? also, just what _is_ "reciprocity" supposed to mean here?? ??did it have soemthing to do with transforming between more than just two basises?? or something?? something about getting the same transformation matrix for two different changes of basis or something??... ??any relationship to situations where "reciprocity" means some sort of "adjointness"?? ...still unsure about which traditional sorts of "reciprocity" get included there... ??lawvere suspected all of them?? ... or something...)

?"derived morita context" as chain complex of bimodules, and "core of a t-structure on a triangulated category" and so forth... ??...

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