Timeline for Reference request : dimensions of real representations of Lie groups
Current License: CC BY-SA 3.0
6 events
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| May 22, 2013 at 14:14 | comment | added | Samuel Tinguely | @Jim Humphrey: I am indeed interested in finite dimentional representations. I am getting more or less comfortable with the theory of complex representations, but when it come to real ones, I have trouble finding good sources. @Livu Nicolaescu: Thanks for this reference, I'll check it out. | |
| May 17, 2013 at 21:21 | comment | added | Jim Humphreys |
@Samuel: From the context I assume you are interested in finite dimensional representations. These are well-studied, but usually indirectly via their Lie algebras and complexifications. As Dietrich points out, the (relatively easy) dimensions depends on Weyl's formula, for compact or complex Lie groups (or Lie algebras). But working with real forms sometimes doubles dimensions, since irreducible over $\mathbb{R}$ may not mean irreducible over $\mathbb{C}$. There are lots of textbooks, but what works best depends on what you know.
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| May 17, 2013 at 18:44 | comment | added | Dietrich Burde | For the dimensions look for Weyl's dimension formula for compact Lie groups. | |
| May 17, 2013 at 15:38 | comment | added | Liviu Nicolaescu | Have a look at the book Representations of compact Lie groups by Brocker and tom Dieck, Grad. Texts in Math, vol. 98, Springer. | |
| May 17, 2013 at 15:37 | answer | added | Peter Michor | timeline score: 4 | |
| May 17, 2013 at 15:02 | history | asked | Samuel Tinguely | CC BY-SA 3.0 |