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Results tagged with lie-groups
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user 74343
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
3
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0
answers
136
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Lagrangian subvariety in coadjoint orbit
In Chriss and Ginzburg's Representation Theory and Complex Geometry, Theorem 3.3.6 says that
"Let $\mathbb{O}$ be a coadjoint orbit in $\mathfrak{g}^*$. Let $x\in \mathbb{O}$ be such that $x|_{\mathf …
- 540
6
votes
2
answers
511
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The Analog of Borel Subgroup in a Compact Real Form
I recently learned that there is a one-to-one correspondence between isomorphism classes of complex reductive groups and isomorphism classes of compact connected real Lie groups given by taking a comp …
- 540
1
vote
0
answers
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Generalized Gaussian Decomposition
Let $G$ be a connected complex semisimple Lie group. Let $H$ be a maximal torus of $G$, let $W$ be the Weyl group of $G$, and let $N_\pm$ be a pair of opposite maximal unipotent subgroups. For each si …
- 540