Timeline for Finite groups in which every character has real values: grading the representations
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 5, 2011 at 18:59 | comment | added | Frieder Ladisch | I unaccepted this answer, since non-degenerateness on isotypic components is not enough, as ndkrempel pointed out. @ndkrempel: I think positive definiteness doesn't work either here since you do not have such a thing for complex reps, and every representation over the reals, no matter of which type, has a positive definite invariant form. | |
| Jan 26, 2011 at 19:45 | comment | added | ndkrempel | For the case of the tensor product of two indicator +1 irreps, it seems you could use positive definiteness + restriction to irreducible subreps to get the result. | |
| Jan 26, 2011 at 19:33 | comment | added | ndkrempel | Ok, but then I don't see how it rules out a direct sum of an indicator -1 irrep with itself, since that supports a non-degenerate symmetric form. | |
| Jan 26, 2011 at 16:55 | comment | added | Ben Webster♦ | If I just randomly restrict to irreducible representations, I believe the form could be become degenerate. At least it's not obvious to me that it's impossible. What is impossible is for it to become degenerate on an isotypic component. | |
| Jan 26, 2011 at 2:32 | comment | added | ndkrempel | I don't understand what you mean by "which must preserve isotypic components". Aren't you restricting the tensor product form to irreducible subrepresentations? And the only thing you have to worry about is the form becoming degenerate (i.e. zero in this case). | |
| Jan 25, 2011 at 15:04 | vote | accept | Frieder Ladisch | ||
| Feb 5, 2011 at 18:44 | |||||
| Jan 25, 2011 at 2:06 | history | answered | Ben Webster♦ | CC BY-SA 2.5 |