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I want to study about Symplectic group actions and moment map, especially Hamiltonian Group Actions. Can you help me with some concretely example of Hamiltonian group actions ? Where can I find some exemple?

edited Mar 14 at 1:13

Claudio Gorodski
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asked Mar 13 at 22:49

danciulian
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I think that if you say what motivated you to learn about Hamiltonian group actions, the answers you'll receive will be specifically suited to your tastes. In any case, you can always look in McDuff-Salamon's symplectic topology book or the notes Claudio provided a link for. – Russell Mar 14 at 4:28

Claudio Gorodski · Accepted Answer · 2013-03-14 01:09:28Z UTC

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I think these http://www.math.ist.utl.pt/~acannas/Books/lsg.pdf are very good notes, and freely available.

answered Mar 14 at 1:09

Claudio Gorodski
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PDC · Answer 2 · 2013-03-13 23:07:05Z UTC

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Consider the representation of $U(1)$ on $\mathbb{C}^n$ defined by $$t\cdot (z_1,\ldots,z_n)=(tz_1,\ldots,tz_n),$$ where $t\in U(1)$. This action is Hamiltonian.

answered Mar 13 at 23:07

PDC
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Furthermore, a moment map is $\mu:\mathbb{C}^n\rightarrow\frak{u}(1)^*\cong\mathbb{R}$, $$\mu(z)=\frac{1}{2}<z,z>,$$ where <,> denotes the standard Hermitian inner product on $\mathbb{C}^n$. – PDC Mar 13 at 23:11

Hamiltonian group actions - examples

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