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- From: kwhyte@dent.uchicago.edu (Kevin Whyte)
- Newsgroups: sci.math
- Subject: Spectum of a Lie group ...
- Message-ID: <1992Oct7.202037.14510@midway.uchicago.edu>
- Date: 7 Oct 92 20:20:37 GMT
- Sender: news@uchinews.uchicago.edu (News System)
- Organization: Dept. of Mathematics, U. of Chicago
- Lines: 17
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- Let G be a compact semi-simple Lie group. The killing
- form gives a canonical Riemannian metric, and hence a
- laplacian acting on smooth functions. What are the eigen-values
- of this laplacian?
-
- L (the laplacian) is a G invariant elliptic operator, on, say
- L2(G). Hence the eigenspaces are finite dimensional and G invariant.
- Peter-Weyl then tells us that each one of these is just some sum
- of irreduciple reps. of G (each of which occurs as many times as
- its weight). Thus, given an irreducible rep. of G, it occurs in at
- most n such eigenspaces (if G is an n dimensional rep.), so it
- should have n positive real numbers associated to it. What are they?
-
- -Kevin
- kwhyte@math.uchicago.edu
-