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 ? > > > > > 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
