From 9a88e9ff0385f66e7c565a394908503dc6e916ad Mon Sep 17 00:00:00 2001 From: neodarz Date: Fri, 28 Apr 2017 00:30:19 +0200 Subject: Site updated at 2017-04-28T00:29:42+02:00 source branch was at: f1965c50670f611ef54f9471490d45a554f7d866 Correct a link --- ...1-19-convolution-of-irreducible-characters.html | 44 ++++++++++++++++++++++ 1 file changed, 44 insertions(+) create mode 100644 build/blog/2014-11-19-convolution-of-irreducible-characters.html (limited to 'build/blog/2014-11-19-convolution-of-irreducible-characters.html') diff --git a/build/blog/2014-11-19-convolution-of-irreducible-characters.html b/build/blog/2014-11-19-convolution-of-irreducible-characters.html new file mode 100644 index 00000000..5b1a90f3 --- /dev/null +++ b/build/blog/2014-11-19-convolution-of-irreducible-characters.html @@ -0,0 +1,44 @@ + + + + + + + +Convolution of irreducible characters + + + + + + + + +
This blog has been archived.
Visit my home page at zhimingwang.org.
+ +
+
+

Convolution of irreducible characters

+
+ +
+
+

TL; DR: The actual PDF write-up is here.

+
+

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 (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.

+
+
+ + + -- cgit v1.2.1