4 ms·
Young Diagrams and Classical Groups [pdf]
- adamnemecek 4y agoThe underlying idea is the idea of fixed points (aka spectra, diagonalizations, embedding, invariants, braids). By fixed point I mean something like the "Lawvere's fixed point theorem". https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theorem https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theore... I have a linkdump on this https://github.com/adamnemecek/adjoint https://github.com/adamnemecek/adjoint I also have a discord https://discord.gg/mr9TAhpyBW https://discord.gg/mr9TAhpyBW
- klysm 4y agoWhat's the discord for?
- adamnemecek 4y agoFurther discussion.
- klysm 4y agoAbout what specifically
- generationP 4y agoThe only two 1-dimensional representations of the symmetric group (i.e., what you can call fixed points if you squint a bit) are the ones that correspond to the partitions (n) and (1,1,...,1), which are the least interesting ones. Everything else is significantly more complicated. It's a block-diagonalization (Young seminormal form) with lots of nontrivial blocks. So no, you won't understand it in terms of fixed points (and certainly not of Lawvere's theorem, which I've never seen used in the entire subject).
- ShuffleBoard 4y agoAwesome! Thank you!
- generationP 4y agoI knew Craige Schensted left his mark on the subject; I had no idea his wife (Irene Verona Schensted) had written a book about it! (well, I think it's about it; it's not on libgen...)