[GAP Forum] a GAP-readable table of the primitive finite subgroups of GL(n, C), for n small?
Dima Pasechnik
dmitrii.pasechnik at cs.ox.ac.uk
Thu Jun 26 13:23:33 BST 2014
On Thu, Jun 26, 2014 at 12:41:23PM +0100, pjc at mcs.st-and.ac.uk wrote:
> It may be worse than you thought. I just got this from Martin Roeteller:
>
> |Dear Peter,
> |
> |I was wrong in three ways: first of all it was not about the
> |classification of crystallographic groups, it was about the
> |finite subgroups of SU(n). And the dimension was not as
> |large as n=20, it was as small as n=3 (!!). And the
> |original classification was not due to Kneser, as I
> |thought, but was due to Blichfeldt.
This seems to be a different story, as SU (rather than GU) adds
complications, and as it's not restricted to primitive linear
groups...
> |
> |The paper is Ludl, "Comments on the classification of the
> |finite subgroups of SU(3)", J Phys A Math Theory 44:255204,
> |2011. Also on the arxiv at http://arxiv.org/abs/1101.2308
> |and http://arxiv.org/abs/1310.3746. Apparently he found
> |missing subgroups, the smallest one being a split extension
> |of order 162.
> |
> |Best,
> |Martin
>
>
> > Dear all,
> >
> > has onyone compiled such a list, which would incorporate the
> > classically known lists due to Blichfeldt for n=4 (with corrections),
> > etc?
> > (in particular the case n=4 is a bit questionable, as there were
> > repeated publications of incomplete lists in this case).
> >
> > Thanks,
> > Dima
> >
> > PS. an irreducible representation of a finite group is called
> > primitive if it is not induced from a representation of a subgroup.
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