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Results tagged with rt.representation-theory
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user 7311
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
43
votes
Is Fourier analysis a special case of representation theory or an analogue?
First, I think it is better to restrict the term "Fourier Analysis" to refer to the process of expanding functions on a locally compact ABELIAN group $G$ as a "sum'' of the characters of the group. ( …
- 15.3k
37
votes
5
answers
5k
views
When are the eigenspaces of the Laplacian on a compact homogeneous space irreducible represe...
I was writing up some notes on harmonic analysis and I thought of a question that
I felt I should know the answer to but didn't, and I hope someone here can help me.
Suppose I have a compact Riemann …
- 15.3k
7
votes
Which Riemannian manifolds admit a finite dimensional transitive Lie group action?
I think that one of the nicest results in this direction may be the one in Ambrose and Singer's paper "On homogeneous Riemannian manifolds". They give a local NASC for a complete Riemannian manifold t …
- 15.3k
5
votes
Finite-dimensional faithful representations of compact groups
Another famous and interesting NASC for a compact (or even locally compact) group to have a faithful finite dimensional representation is that it "not have arbitrarily small subgroups", i.e., that the …
- 15.3k