Timeline for What are the 4-dimensional complex representations of the real group GL(4,R)?
Current License: CC BY-SA 4.0
12 events
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| Dec 14, 2022 at 18:09 | history | edited | Ben Webster♦ | CC BY-SA 4.0 |
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| Dec 14, 2022 at 18:09 | comment | added | Ben Webster♦ | @RobertBryant You're right; I'd dealt with that previously, and then messed it up fixing another mistake. Sigh. | |
| Dec 13, 2022 at 22:07 | comment | added | Robert Bryant | @BenWebster: Yah, I didn't think it would really change the answer, but I didn't want the OP to be confused. Thanks for fixing it. Also, for some reason the OP asked for 4-dimensional complex representations, so I guess that you'd want to include representations such as $\rho(A) = e^{\lambda\,\log|\det(A)|} A$ where $\lambda$ is a complex number with nonzero imaginary part. | |
| Dec 13, 2022 at 20:31 | comment | added | Ben Webster♦ | @RobertBryant Now it's fixed; it actually doesn't change the answer, since the irrep $\mathbb{R}^4$ is already the restriction of an irrep of $GL(4;\mathbb R)$. | |
| Dec 13, 2022 at 20:30 | history | edited | Ben Webster♦ | CC BY-SA 4.0 |
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| Dec 13, 2022 at 16:24 | comment | added | Ben Webster♦ | Oy vey, this is hard to get right for such an "easy" question. Of course you’re right… | |
| Dec 12, 2022 at 15:54 | comment | added | Robert Bryant | I know that this is being picky, but it's not true that $\mathrm{GL}(4,\mathbb{R})\simeq \mathrm{SL}(4,\mathbb{R})\times \mathbb{R}^{\times}$. Where would $A = \mathrm{diag}(-1,1,1,1)$ go under such an isomorphism? | |
| Dec 12, 2022 at 1:56 | history | edited | Ben Webster♦ | CC BY-SA 4.0 |
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| Dec 12, 2022 at 1:30 | history | edited | Ben Webster♦ | CC BY-SA 4.0 |
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| Dec 12, 2022 at 1:05 | comment | added | paul garrett | Ok, and... what's the easy explanation? :) | |
| Dec 12, 2022 at 0:57 | comment | added | YCor | You can probably also twist irreducible ones by a character (and also consider various non-irreducible ones with abelian image). | |
| Dec 12, 2022 at 0:35 | history | answered | Ben Webster♦ | CC BY-SA 4.0 |