[HN Gopher] Young Diagrams and Classical Groups [pdf]
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Young Diagrams and Classical Groups [pdf]
Author : gbrown_
Score : 33 points
Date : 2022-09-25 11:24 UTC (1 days ago)
(HTM) web link (math.ucr.edu)
(TXT) w3m dump (math.ucr.edu)
| ShuffleBoard wrote:
| Awesome! Thank you!
| generationP wrote:
| I 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...)
| adamnemecek wrote:
| The 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
| generationP wrote:
| 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).
| klysm wrote:
| What's the discord for?
| adamnemecek wrote:
| Further discussion.
| klysm wrote:
| About what specifically
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