On Monday, August 20, 2012 1:41:42 PM UTC-5, John H Palmieri wrote: > > > > On Monday, August 20, 2012 11:21:04 AM UTC-7, bsmile wrote: >> >> >> >> On Monday, August 20, 2012 12:56:07 PM UTC-5, John H Palmieri wrote: >>> >>> >>> >>> 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? >> > > Use a different partition. Every partition of 4 will give an irreducible > representation. You can get each of the representations like this: > > sage: [SymmetricGroupRepresentation(p) for p in Partitions(4).list()] >
Thanks, this exactly gives what I am trying to calculate. Summarizing your input and I learned to write the following, sage: S4=SymmetricGroup(4) sage: S4.character_table() sage: rep=SymmetricGroupRepresentation([2,2]) sage: REPS=[(p,rep(p)) for p in S4] sage: REPS It seems REPS now saves an irreducible 2D matrix representation for S4. Can I ask further, (1) what's the advantages towards each of the three options, "specht", "orthogonal", "seminormal" for SymmetricGroupRepresentation? It seems "orthogonal" gives something matching the physically meaningful Td group result. (2) How can I output to file so that fortran can directly read in the matrices for subsequent calculation? (3) Is there a nice way to print the output on the screen so that the matrix is clearly seen? It seems REPS=[rep(p) for p in S4] would do pretty good, but I will lose track of which element corresponds to which matrix. (4) Is there command in SAGE so that I can use to check that the REPS really gives a representation for the S4 group? Thanks a lot! Sincerely, Jon > > -- > 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
