Timeline for Finite groups in which every character has real values: grading the representations
Current License: CC BY-SA 2.5
13 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Feb 14, 2011 at 17:49 | comment | added | Zoltan Zimboras | I just read your counter examples. Thanks for them!! Then this question is settled. I'm now thinking of Greg Kuperberg's question, whether one can "point out" in which cases (or for which large families of finite and compact groups) this grading still exists. (I was also thinking of looking at compact simple Lie groups). | |
| Feb 13, 2011 at 15:34 | comment | added | Frieder Ladisch | The counterexample Qiaochu asks for would actually settle the question, so I'm interested in that, too. However, your answer shows that the weaker statement we already have has interesting applications, too. | |
| Feb 13, 2011 at 15:28 | comment | added | Frieder Ladisch | As you stated it, the extension to groups with complex irreps is actually wrong: The group $SL(2,3)$ has a unique symplectic irrep. Multiplying its character with the complex linear characters yields irreps with FS-indicator 0. True is the following: in a tensorproduct of a complex irrep with its dual, symplectic irreps occur with even multiplicity. As far as I can follow the paper you linked, their main result is the extension of this to more than two factors, and for more general categories. | |
| Feb 13, 2011 at 9:59 | comment | added | Zoltan Zimboras | And do you know of any nice example, where there appears a symplectic irrep in the tensor product of two real irreps? Because I haven't found any yet (to answer also to Qiaochu's question), although I haven't thought much about this. | |
| Feb 12, 2011 at 18:40 | comment | added | Frieder Ladisch | Thanks for your answer, Zoltan. I figured out the extension to groups with complex irreps myself when trying to prove the FS-indicator-grading (I did this only in the context of finite groups, however). | |
| Feb 12, 2011 at 1:25 | comment | added | Qiaochu Yuan | @Zoltan: do you actually have a counterexample for the nonexistence of the FS-indicator grading? I suspected this but don't know of good examples. | |
| Feb 11, 2011 at 21:03 | history | edited | Zoltan Zimboras | CC BY-SA 2.5 |
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| Feb 11, 2011 at 20:57 | history | edited | Zoltan Zimboras | CC BY-SA 2.5 |
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| Feb 11, 2011 at 20:40 | history | edited | Zoltan Zimboras | CC BY-SA 2.5 |
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| Feb 11, 2011 at 20:22 | history | edited | Zoltan Zimboras | CC BY-SA 2.5 |
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| Feb 11, 2011 at 20:06 | history | edited | Zoltan Zimboras | CC BY-SA 2.5 |
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| Feb 11, 2011 at 19:50 | history | answered | Zoltan Zimboras | CC BY-SA 2.5 |