Hi, sorry for joining this discussion late; I found your thread by accident just recently. If you want to look at the irreducible representation matrices of the symmetric group you can find them in the attached package. Maybe that helps!

Attachments:

CharachtersSymGrp12.nb

IrrCharSymGrp.m

I will certainly send you a copy when I have it ready. However, on each iteration I have been cutting back on the group theoretical details in order to make the paper more useful to those teaching lower-level courses in quantum mechanics.

My question "where do you find..." was using the "ask first think later" protocol. " which is always dumb. I am using S3 as an example in a pedagogical paper on identical particles in quantum mechanics. After looking at your codes I finally realized that the Permutations function does all I need for my example. Thanks again for your help

Hmmm, once I used to program a lot concerning group theory. One of the problems was enumerating substitutional isomers of a given molecule. See J.Chem.Inf.Comput.Sci. 2000, 40, 956-966. In fact I cannot say "where to find this stuff", I just remembered what I was doing then.

Kind regards, HD

Or more compact

n = 3;
ge = Permutations[Range[n]]  (* the elements of S3  *)

(* Multiplication of group-elements *)

gp[a_, b_] := Module[{},
gL = Length[a];
Table[a[[b[[j]]]], {j, 1, gL}]]   

(* Make Matrix for regular representation *)

gm[a_] := Module[{},
  gLg = Length[ge];
  mm = Table[0, {i, gLg}, {j, gLg}];
  j = 1;
  While[
   j <= gLg,
   gxg = gp[a, ge[[j]]];
   mm[[j, Position[ge, gxg][[1, 1]]]] = 1;
   j = j + 1
   ];
  mm
  ]

And finally

MatrixForm /@ (gm /@ ge)

Thanks for the useful lead. I was hoping for a canned Mathematica code that would, for example, generate the matrices of the regular representation of say S3. I guess I am getting lazy in my old age. I did the job myself by brute force, but I suspect that a variation of your code would do the trick more elegantly..