From 785bde84dd4888817bb9825ba5ab388ec2b7c4b7 Mon Sep 17 00:00:00 2001 From: neodarz Date: Thu, 4 May 2017 03:27:33 +0200 Subject: Update to date --- .../2014-11-19-convolution-of-irreducible-characters.md | 15 --------------- 1 file changed, 15 deletions(-) delete mode 100644 source/blog/2014-11-19-convolution-of-irreducible-characters.md (limited to 'source/blog/2014-11-19-convolution-of-irreducible-characters.md') diff --git a/source/blog/2014-11-19-convolution-of-irreducible-characters.md b/source/blog/2014-11-19-convolution-of-irreducible-characters.md deleted file mode 100644 index 7466b1cd..00000000 --- a/source/blog/2014-11-19-convolution-of-irreducible-characters.md +++ /dev/null @@ -1,15 +0,0 @@ ---- -title: "Convolution of irreducible characters" -date: 2014-11-19T20:40:37-0800 -date_display: November 19, 2014 ---- - -__*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). -- cgit v1.2.1