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Results tagged with rt.representation-theory
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user 7392
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
0
votes
Fourier series for the Heisenberg nilmanifold
You might find what you need in Starkov's "Dynamical systems on homogeneous spaces", in the chapter "Spectral theory of homgoeneous flows". Apparently he analyzes the case of an ergodic flow on a nilm …
- 4,874
10
votes
1
answer
1k
views
Which groups can be recovered from their unitary dual?
Note: in this post, every topological group under consideration is assumed to be Hausdorff.
Given a locally compact abelian group, one can construct its dual group, i.e. its group of (unitary) charac …
- 4,874
13
votes
Accepted
Finite-dimensional faithful representations of compact groups
A famous theorem is that this is true if and only if $G$ is a Lie group.
- 4,874
7
votes
2
answers
1k
views
Decomposing an arbitrary unitary representation of a connected nilpotent Lie group in terms ...
For a locally compact (Hausdorff) abelian group $G$ we have following theorem (see e.g. Folland):
"For every (strongly continuous) unitary representation $(\pi,\mathcal{H_{\pi}})$ of $G$, there exist …
- 4,874