On Monday, August 20, 2012 12:56:07 PM UTC-5, John H Palmieri wrote: > > > > On Monday, August 20, 2012 10:36:54 AM UTC-7, David Joyner wrote: >> >> 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!! >> > > I don't know much about this aspect of Sage, but you can also try this: > > sage: rep = SymmetricGroupRepresentation([3,1]) > > Now rep is the representation of S_4 (since 4=3+1) corresponding to the > partition [3,1]. We can compute find the matrix associated to each element > of S_4: > > sage: rep([1,4,3,2]) > [ 1 0 0] > [ 1 -1 1] > [ 0 0 1] > sage: REPS = [(x,rep(x)) for x in S4.list()] > > This defines REPS to be a list of pairs, (elt of S_4, corresponding > matrix). > > Is that the sort of thing you want? >
Thanks for your response. It's close, but not quite. It seems the way you pointed out does give a 3D irreducible matrix representation for S4. But how can I get the 2D irreducible matrix representation for S4? > > -- > John > > -- -- 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
