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states that any invariant eigendistribution, and in particular any character of an irreducible unitary representation on a
Hilbert space, is given by a
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that is invariant under conjugation, and is an eigendistribution of the center of the
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that is analogous to the character of a finite-dimensional representation of a
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Representation Theory of
Semisimple Groups: An Overview Based on Examples.
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297:{\displaystyle \Theta _{\pi }:f\mapsto \operatorname {Tr} (\pi (f))}
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227:{\displaystyle \pi (f)=\int _{G}f(x)\pi (x)\,dx}
43:but its sources remain unclear because it lacks
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128:Suppose that π is an irreducible
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385:Representation theory of Lie groups
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342:of the representation π.
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