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| author | Zhiming Wang <zmwangx@gmail.com> | 2015-05-04 14:55:10 -0700 |
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| committer | Zhiming Wang <zmwangx@gmail.com> | 2015-05-04 14:55:10 -0700 |
| commit | 301679861a2440a10c9eac746cec86459f445ef9 (patch) | |
| tree | 5aad22ead01cf0da226623f603f33867896c0fea /source/_posts/2014-11-19-convolution-of-irreducible-characters.md | |
| parent | d0a07c64afba47bbe8bfb56ba9893296a73fc7db (diff) | |
| download | my_new_personal_website-301679861a2440a10c9eac746cec86459f445ef9.tar.xz my_new_personal_website-301679861a2440a10c9eac746cec86459f445ef9.zip | |
remove all Octopress stuff
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| -rw-r--r-- | source/_posts/2014-11-19-convolution-of-irreducible-characters.md | 16 |
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diff --git a/source/_posts/2014-11-19-convolution-of-irreducible-characters.md b/source/_posts/2014-11-19-convolution-of-irreducible-characters.md deleted file mode 100644 index f3f3207e..00000000 --- a/source/_posts/2014-11-19-convolution-of-irreducible-characters.md +++ /dev/null @@ -1,16 +0,0 @@ ---- -layout: post -title: "Convolution of irreducible characters" -date: 2014-11-19 20:40:37 -0800 -comments: true -categories: ---- -__*TL; DR:* The actual PDF write-up is [here](https://dl.bintray.com/zmwangx/generic/20141119-convolution-of-irreducible-characters.pdf).__ - ---- - -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. - -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). |