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### When does a symmetric Poisson manifold decompose into homogeneous pieces?

When people study representations, they pay a lot of attention to the irreducible ones. This is justified by the fact that, roughly speaking, every unitary representation decomposes into a direct ...

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### classification for coadjoint orbits of lower or upper triangular matrices

Is there any classification for coadjoint orbits of lower or upper triangular matrices in general case $n\times n$. Is there any reference?

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### Is there algebraic structure (manifold, stack …) on the SET of irreducible representation of algebraic group ?

Consider algebraic group G over some field "k".
Consider the SET of all its complex irreducible representations (I think I need unitary also).
Question Is there some way to put algebraic structure ...

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### Geometric interpretation of Universal enveloping algebras

Given a complex Lie algebra $\mathfrak g$, we can form its universal enveloping algebra and interpret it as a noncommutative space.
Is this perspective useful? What does this space "look like"?
How ...