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.
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
