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| author | Zhiming Wang <zmwangx@gmail.com> | 2015-05-04 18:45:17 -0700 |
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| committer | Zhiming Wang <zmwangx@gmail.com> | 2015-05-04 18:45:17 -0700 |
| commit | 07bf43a314fe65ccd9c7cb663c3c6134a47cc269 (patch) | |
| tree | 93104d3f07143b1e62d773d95dd973888cdd7f27 /source/blog/2014-11-19-convolution-of-irreducible-characters.md | |
| parent | ee374553f2ba385157eec9a816cf9b023fbfb18a (diff) | |
| download | my_new_personal_website-07bf43a314fe65ccd9c7cb663c3c6134a47cc269.tar.xz my_new_personal_website-07bf43a314fe65ccd9c7cb663c3c6134a47cc269.zip | |
edit posts and (mostly) figured out the theme
Also wrote pyblog that currently can generate parts most of the blog.
Diffstat (limited to 'source/blog/2014-11-19-convolution-of-irreducible-characters.md')
| -rw-r--r-- | source/blog/2014-11-19-convolution-of-irreducible-characters.md | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/source/blog/2014-11-19-convolution-of-irreducible-characters.md b/source/blog/2014-11-19-convolution-of-irreducible-characters.md index 58a58925..9b95ca94 100644 --- a/source/blog/2014-11-19-convolution-of-irreducible-characters.md +++ b/source/blog/2014-11-19-convolution-of-irreducible-characters.md @@ -9,6 +9,6 @@ __*TL; DR:* The actual PDF write-up is [here](https://dl.bintray.com/zmwangx/gen Yesterday I was trying to establish the formula for orthogonal primitive central idempotents of a group ring. It is possible to establish the result through the convolution of irreducible characters. However, I stuck quite a while on trying to work out the convolutions themselves. For a formidable and unenlightening proof using "matrix entry functions" (i.e., fix a basis, induce a matrix representation, and explicitly expand everything in matrix elements), see [this post](http://drexel28.wordpress.com/2011/03/02/representation-theory-using-orthogonality-relations-to-compute-convolutions-of-characters-and-matrix-entry-functions/) (in fact, this is just one in a series of posts that lead up to the result). That's a really sad proof. -It turns out that I really should have been working the other way round --- first establish the orthogonal idempotents (the proof of which is really simple and elegant, I was just trapped in a single thread of thought), then use that to compute the convolution of irreducible characters. +It turns out that I really should have been working the other way round — first establish the orthogonal idempotents (the proof of which is really simple and elegant, I was just trapped in a single thread of thought), then use that to compute the convolution of irreducible characters. I feel like this is worth presenting (as the only proof I saw online is the really sad one above), so I TeX'ed it up. I tried to convert to MathJax HTML but eventually gave up (that's the story for another post). So, the write-up is in good ol' PDF, available [here](https://dl.bintray.com/zmwangx/generic/20141119-convolution-of-irreducible-characters.pdf). |