Questions tagged [orbit-method]

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Spectral decomposition of the automorphic space for a unipotent group

Let $k$ be a global field of positive characteristic, $\mathbb{A}$ its adele ring. Let $U$ be a unipotent algebraic group over $k$, of dimension sufficiently small relative to ${\rm char} (k)$. Is ...
Sasha's user avatar
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2 votes
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A representation similar to coadjoint representation?

In a project of quantization, I come up with a finite dimensional representation of $so(d)$ that I wish to find some decent references for it. I guess it could have been studied thoroughly in ...
whitejet's user avatar
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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 ...
Vectornaut's user avatar
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5 votes
2 answers
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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 (...
Alexander Chervov's user avatar
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4 answers
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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 ...
Jan Weidner's user avatar
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