A helpful further response from Marc Keilberg indicates that this is possible for finite G.
Concretely, I'm working with $S_n$, which I should have clarified. If anyone can spell out what I need to do to get back $g$ (as opposed to just its class representative) that would be enormously helpful. Best wishes, Jerry. On Sun, Jun 18, 2017 at 2:30 PM, Marc Keilberg <keilb...@usc.edu> wrote: > Eh, jumped the gun. So used to working with characters I failed to > realize these are the full representations you're applying. In this case, > at least for finite G: yes. A faithful permutation representation of the > group is determined by the representation theory (you can write it out in > permutation matrices, in particular), and the group elements are uniquely > determined by their representation as a permutation. > > On Sun, Jun 18, 2017 at 6:11 AM, Marc Keilberg <keilb...@usc.edu> wrote: > >> The irreducible characters are class functions, so you necessarily can't >> get any more information than the conjugacy class. And since the >> irreducible characters are a basis for the class functions, that's >> precisely what you can recover. So you can only recover g itself if it's >> in the center. >> >> On Sun, Jun 18, 2017 at 6:05 AM, Jerry Swan <dr.jerry.s...@gmail.com> >> wrote: >> >>> Dear all, >>> >>> For some element g of a group G for which irr := >>> IrreducibleRepresentations(G) have been obtained, is it possible to >>> recover >>> g from images := List(irr,r->Image(r,g)) ? >>> >>> Best wishes, >>> >>> Jerry. >>> _______________________________________________ >>> Forum mailing list >>> Forum@mail.gap-system.org >>> https://urldefense.proofpoint.com/v2/url?u=http-3A__mail.gap >>> -2Dsystem.org_mailman_listinfo_forum&d=DwICAg&c=clK7kQUTWtAV >>> EOVIgvi0NU5BOUHhpN0H8p7CSfnc_gI&r=_TYxCHNDVTm_qGVCLj17bw&m=y >>> 4nrJdKFNr9joQ1eeYyehMaJ2p3PMu99Y93s2YNwjHA&s=8bZHZiY2EuP7o6n >>> TtyHlnR2WWi_zZJl9kDPTA0doM4o&e= >>> >> >> > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
