Timeline for Does a quotient group $G/N$ have a natural action on the regular representation of $G$?
Current License: CC BY-SA 3.0
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| Aug 23, 2017 at 11:47 | comment | added | Tobias Kildetoft | The closest I can think of is something like writing the regular rep as the sum of the $N$-fixed points (which is a submodule for $G$) and the rest (this is canonical since the first part is really the $G/N$-reps, so it is a sum of isotypic components). Then one could just define $G/N$ to act trivially on the rest (I am not sure one can do much better than that). | |
| Aug 23, 2017 at 11:39 | comment | added | Ruben Verresen | @GregoryArone Thanks for the question. No, it does not. More precisely, I am just relying on an intuitive notion of 'natural', but this might have a precise version from some category theory perspective, which I simply don't know enough about. | |
| Aug 23, 2017 at 9:54 | comment | added | Gregory Arone | Does "natural' have a precise meaning here? | |
| Aug 23, 2017 at 0:29 | history | asked | Ruben Verresen | CC BY-SA 3.0 |