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Results tagged with lie-groups
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user 9970
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
2
votes
Connectedness of Springer Fibers
Yes: this is discussed in Chriss & Ginzburg 'Representation Theory and Complex Geometry', p.161 Remark 3.3.26. In short, the nilpotent cone is normal and we can apply Zariski's Main Theorem to deduce …
- 1,201
2
votes
Accepted
Nilpotent Lie Algebras
Whenever $ad_{\xi}$ is an endomorphism of $\mathfrak{g}$ whose corresponding partition $\pi: 1^{s_{1}}2^{s_{2}} \cdots \;$ of $\dim \mathfrak{g}$ is such that $s_{1} =0$, then we have $im\; ad_{\xi} \ …
- 1,201
4
votes
About the intrinsic definition of the Weyl group of complex semisimple Lie algebras
Yes: this is the approach to defining the 'abstract Weyl group' introduced in "Representation Theory and Complex Geometry" by Chriss/Ginzburg on p. 135 (2nd Edition, Birkhauser).
- 1,201