How to obtain real irreducible representation matrices for finite point groups? I would like to generate the irreducible representation matrices in real (not complex) form for any finite point group, in order to use them in a projection operator. At least I require the diagonal elements (not its sum) of the representations. does any one have a clue of how to obtain them?, a reference or whatever is welcome. Thanks in advance.

At least for icosahedral groups (I, Ih), I found the real matrix representations documented in the papers:

1. Pramana – J. Phys., Vol. 79, No. 6, 1365–1373 (DOI:10.1007/s12043-012-0334-1)
2. J. Chem. Inf. Comput. Sci. 2003, 43, 1763-1770 (DOI:10.1021/ci025614x)
3. Superlattices and Microstructures,Volume 3, Issue 4,1987, 391-398 (DOI:10.1016/0749-6036(87)90212-6)



3 years ago I did generate the real tables by myself by means of realizing a similarity transformation of the complex tables generators of Altmann and Herzig though. And I just very recently found the 1st and 2nd papers by chance :'D