On Mon, Aug 20, 2012 at 12:58 PM, bsmile <[email protected]> wrote: > > > 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]> 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]]);
You might want to look at the documentation of that package. > >> > >> > >> > >> > >> > 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] >> > 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 >> > >> > >> > > > -- > -- > 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 > > > -- -- 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
