Timeline for Which groups have only real and quaternionic irreducible representations?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2010 at 5:49 | history | edited | Torsten Ekedahl | CC BY-SA 2.5 |
deleted 4 characters in body
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| Nov 28, 2010 at 4:52 | comment | added | John Baez | Torsten wrote: "All representations are real-valued precisely when..." I think it might be a bit clearer to say "All characters are real-valued precisely when..." | |
| Nov 27, 2010 at 16:28 | comment | added | John Baez | Thanks, Torsten and André. I guess for type $D$ I can just think about the spinor reps (which I actually know and love) and figure out when they're real or quaternionic; all the other fundamental reps are real, since they're exterior powers of the tautologous rep of $SO(n)$ on $\mathbb{R}^n$. | |
| Nov 27, 2010 at 16:24 | vote | accept | John Baez | ||
| Nov 27, 2010 at 14:17 | comment | added | André Henriques | Otherwise, the difference between $w_0$ and $-1$ is measured by the outer automorphism of $G$ that acts as $g\mapsto -g$ for $g\in Z(G)$. | |
| Nov 27, 2010 at 14:02 | comment | added | André Henriques | $w_0 = -1$ if and only if the center of the ( simply connected semisimple) Lie group is isomorphic to $(\mathbb Z/2)^k$ for some $k\ge 0$. | |
| Nov 27, 2010 at 12:20 | history | edited | Torsten Ekedahl | CC BY-SA 2.5 |
Precise conditions for the connected case
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| Nov 27, 2010 at 11:34 | history | answered | Torsten Ekedahl | CC BY-SA 2.5 |