Timeline for Density and irreducibility
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Oct 30, 2010 at 19:12 | comment | added | Jim Humphreys | @unknown Mixing Lie group and algebraic group language is risky, as when you take matrix groups over the reals as examples: these are better viewed as the real points of certain algebraic groups (or group schemes). The Zariski topology comes into play when you look at polynomial or rational function properties, so "faithful irreducible representation" in the question should refer to a "rational" (algebraic group) representation. | |
| Oct 30, 2010 at 7:38 | answer | added | Makoto Yamashita | timeline score: 1 | |
| Oct 30, 2010 at 6:15 | answer | added | Greg Kuperberg | timeline score: 3 | |
| Oct 30, 2010 at 5:49 | history | edited | user9552 | CC BY-SA 2.5 |
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| Oct 30, 2010 at 4:14 | comment | added | user9552 | Yes G comes with a faithful irreducible representation. For example we can take G=SL(n,R) or SO(n,R). In these cases subgroup H being irrreducible means when H acts on R^n there is no nontrivial invariant subspaces. | |
| Oct 30, 2010 at 2:42 | comment | added | Allen Knutson | Subspaces of what? Does G come with a faithful irrep, that remains irreducible for H? In which case you want somehow to exclude G = the circle. | |
| Oct 30, 2010 at 2:24 | history | asked | user9552 | CC BY-SA 2.5 |