Skip to main content
MathOverflow

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

Required fields*

4
  • 4
    $\begingroup$ Maybe (?) an equivalent form of the answer is that because $Z_G\rightarrow G/(G, G)$ has finite kernel, after twisting by a character the representation becomes trivial on a finite index subgroup of $Z_G$. Therefore the assertion follows from the same proposition in Serre’s book :p $\endgroup$ Commented Jan 22 at 9:27
  • $\begingroup$ @Cheng-ChiangTsai that's a very nice argument! $\endgroup$ Commented Jan 22 at 9:33
  • $\begingroup$ @KentaSuzuki I remarked that u can also use the preimage of the image of $\Gamma\subset PGL(V)$ under the surjective morphism $SL(V)\to PGL(V)$. $\endgroup$ Commented Jan 22 at 17:49
  • 1
    $\begingroup$ @KentaSuzuki Yay! I still feel like the related elements appeared in your talk two weeks ago :p $\endgroup$ Commented Jan 23 at 2:35