Timeline for Finite groups such that every irrep can be induced from trivial irrep of a subgroup ?
Current License: CC BY-SA 3.0
7 events
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| Aug 28, 2012 at 15:40 | comment | added | Jim Humphreys | @Alexander: Constructing headers is an art form, I fear ;-) Concerning groups of Lie type like general linear groups, it's not rewarding to study each one in isolation. For a Lie family the BN-structure gives the best hope of using induction methods efficiently from large proper subgroups. Only subgroups related to Lie structure seem useful for study of an entire family. (But my "answer" isn't a direct answer to your question, only an indirect way to ask how useful the question is.) | |
| Aug 28, 2012 at 12:17 | comment | added | Alexander Chervov | "In any case, your header does suggest that you want the induced representations involved to be irreducible, which misleads people at first." May I ask yours advise - yes, I understand title may mislead, but on the other hand it is already too long ... So it is always bothers me - should I the title be precise or I can abbreviate it for shortness scarifying the clarity ? | |
| Aug 28, 2012 at 12:15 | comment | added | Alexander Chervov | @Jim thank you for yours answer. Indeed part of motivation to ask is - parabolic induction - why should we restrict to parabolic subgroups ? I guess it is because it is class of the subgroup which is present on the regular basis for all Lie groups ? However, is the end of the story or someone can someday to come with another class of subgroups ? | |
| Aug 27, 2012 at 0:42 | comment | added | Jim Humphreys | @Will: In my first line, I meant to write "parabolic" but didn't, so I've corrected that. I didn't really intend to exhibit a specific counterexample; my caveat meant to indicate that it doesn't really help in constructing character tables (especially for Lie families) just to know in principle that all irreducible characters might show up somehow by inducing trivial characters of subgroups (i.e., permutation characters on cosets). Aside from that, my problem with the header is that it does make the question look silly at first sight as you point out. | |
| Aug 27, 2012 at 0:33 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Aug 26, 2012 at 23:06 | comment | added | Will Sawin | Induced representations of trivial representations are irreducible only when they're trivial, so that version would be a very silly questions. | |
| Aug 26, 2012 at 22:30 | history | answered | Jim Humphreys | CC BY-SA 3.0 |