On Monday, August 20, 2012 11:30:17 AM UTC-5, David Joyner wrote: > > On Mon, Aug 20, 2012 at 11:46 AM, bsmile <[email protected] <javascript:>> > wrote: > > Thanks, Volker, This is by far I can get by studying the manual and help > > document. But I still cannot get the corresponding irreducible matrix > > representations, and to which group element each representation and > > character correspond to. Can you help me further on it? I was told from > GAP > > forum that SAGE is able to give matrix representation in real numbers, I > > hope I can successfully achieve this with SAGE. > > > > Do you mean this > http://www.gap-system.org/Packages/repsn.html ? > > Sorry, I don't know which package it is, but the command would be something like the following in GAP to get irreducible matrix representations
gap> gr := SymmetricGroup(4);; gap> reps := IrreducibleRepresentations(gr);; gap> List(gr,x->[x,x^reps[3]]); > > > > > > > > > On Monday, August 20, 2012 12:17:50 AM UTC-5, Volker Braun wrote: > >> > >> sage: S7 = SymmetricGroup(7) > >> sage: S7.character_table() > >> [ 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 -1 1] > >> [ 6 -4 2 0 3 -1 -1 0 -2 0 1 1 1 0 -1] > >> [14 -6 2 -2 2 0 2 -1 0 0 0 -1 -1 1 0] > >> [14 -4 2 0 -1 -1 -1 2 2 0 -1 -1 1 0 0] > >> [15 -5 -1 3 3 1 -1 0 -1 -1 -1 0 0 0 1] > >> [35 -5 -1 -1 -1 1 -1 -1 1 1 1 0 0 -1 0] > >> [21 -1 1 3 -3 -1 1 0 1 -1 1 1 -1 0 0] > >> [21 1 1 -3 -3 1 1 0 -1 -1 -1 1 1 0 0] > >> [20 0 -4 0 2 0 2 2 0 0 0 0 0 0 -1] > >> [35 5 -1 1 -1 -1 -1 -1 -1 1 -1 0 0 1 0] > >> [14 4 2 0 -1 1 -1 2 -2 0 1 -1 -1 0 0] > >> [15 5 -1 -3 3 -1 -1 0 1 -1 1 0 0 0 1] > >> [14 6 2 2 2 0 2 -1 0 0 0 -1 1 -1 0] > >> [ 6 4 2 0 3 1 -1 0 2 0 -1 1 -1 0 -1] > >> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] > >> sage: S7.irreducible_characters()[4] > >> Character of Symmetric group of order 7! as a permutation group > >> sage: list(_) > >> [15, -5, -1, 3, 3, 1, -1, 0, -1, -1, -1, 0, 0, 0, 1] > >> > >> > >> On Monday, August 20, 2012 12:51:04 AM UTC-4, bsmile wrote: > >>> > >>> I need to calculate very simple properties of the symmetric group, say > >>> list group elements, their characters and irreducible representations. > Would > >>> you please let me know the related commands to achieve these goals? > Thank > >>> you very much!! > > > > -- > > -- > > To post to this group, send email to > > [email protected]<javascript:> > > To unsubscribe from this group, send email to > > [email protected] <javascript:> > > For more options, visit this group at > > http://groups.google.com/group/sage-support > > URL: http://www.sagemath.org > > > > > > > -- -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
