Young Diagrams and Classical Groups [pdf]
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Young Diagrams and Classical Groups [pdf]
1–8 of 8 posts
Re: Young Diagrams and Classical Groups [pdf]
#2The 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+theore...
I have a linkdump on this
https://github.com/adamnemecek/adjoint
I also have a discord https://discord.gg/mr9TAhpyBW
Re: Young Diagrams and Classical Groups [pdf]
#3Awesome! Thank you!
Re: Young Diagrams and Classical Groups [pdf]
#4The 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+theore... I have a linkdump on this https://github.com/adamnemecek/adjoint I also have a discord https://discord.gg/mr9TAhpyBW
What's the discord for?
Re: Young Diagrams and Classical Groups [pdf]
#5The 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+theore... I have a linkdump on this https://github.com/adamnemecek/adjoint I also have a discord https://discord.gg/mr9TAhpyBW
What's the discord for?
Further discussion.
Re: Young Diagrams and Classical Groups [pdf]
#6The 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+theore... I have a linkdump on this https://github.com/adamnemecek/adjoint I also have a discord https://discord.gg/mr9TAhpyBW
The 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).
Re: Young Diagrams and Classical Groups [pdf]
#7I 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...)