# Tagged Questions

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### Recommended textbooks for Hamiltonian group actions?

I am doing a project on Hamiltonian group actions on symplectic manifolds, and my supervisor was able to list several good books on Riemannian geometry to start me off, but he didn't know of any ...
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### Orbits that 'coalesce'

Let $R$ be a commutative ring, $G$ a group scheme over $\mathrm{Spec}\;R$, and $X$ a scheme over $\mathrm{Spec}\;R$ on which $G$ acts $R$-morphically via $G\times X\to X$. Suppose $S$ is another ...
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### What are the conjugacy classes in $\mathrm{Aut}(G)$?

Let $G$ be an arbitrary group, and let $\mathrm{Aut}(G)$ be the group of automorphisms of $G$ (with composition of morphisms as multiplication). I'd like to learn more about the problem of ...
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### Eigenbundle decomposition

Let $G$ be a finite cyclic group and $X$ a smooth manifold equipped with a trivial $G$-action. It is known that we can decompose every $G$-equivariant vector bundle with respect to the action: ...
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### Group action on a manifold with finitely many orbits

I'm looking for a result along the lines of the following: Let $G$ be a group acting on a set $X$. If the action partitions $X$ into finitely many $G$-orbits, then $\dim G \geq \dim X$. For ...
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### What does “lifted action” mean?

I read about angular moment and linear moment but I don't know what "lifted action" means. Can you explain please? Thanks. :)
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### Hyperbolic spheres in the Poincare half-plane and fractional linaear transformations

Let $\mathbb{H}$ be the Poincare upper half-plane, seen as a Riemannian manifold with the metric $$\frac{dx^2+dy^2}{y^2}.$$ Moreover, we consider the action of $\text{SL}_2(\mathbb{R})$ on ...
### Invariants of binary forms under a $\begin{pmatrix} 1& 1 \\ 0& 1 \end{pmatrix}$ action
The special linear group $\text{SL}_2(\mathbb{Z})$ of $2\times 2$ invertible matrices in $\mathbb{Z}$ acts on binary cubic forms $\{ax^3 + bx^2y + cxy^2 + dy^3\}$ by acting on the vector $(x,y)^T$. ...