29 Feb 2008 From: Jutho.Haegeman [snail] ugent.be A am I PhD student from the University of Ghent. For my research, I need the irreducible representations of the orthogonal group. The final goal is to construct the excited states of the Gross Neveu model on the lattice, which behave as rank r anti-symmetrical tensor reps of O(2N). To do these calculations I follow the approach of chapter 5, and thus I need the 6j and 3j symbols for the tensorial irreps of O(2N). As I am not aware of computational software that can calculate these quantities, I tried to program it myself. I implemented a way to work with O(N) birdtracks (undirected lines, with possible contractions) into Matlab, and was able to construct the projection operators for the tensorial irreps. For this, I use the method described in chapter 10 of your webbook, starting from the Young Projectors of the U(n) irreps, I first project out all possible contractions (by sandwiching the contraction operator between the two young projectors). I guess my implementation is correct, as I am possible to obtain the exact irrep dimensions (for general O(n)) of all the irreps which are present in the decomposition of V^4. I still have two questions: 1) My current implementation is relatively slow, to construct the projection operators for the irreps of the rank 4 tensors I already need a few minutes, for the rank 5 tensors a few hours. This is due to the fact that i try to project out all possible contractions (starting with the highest number) combined with all possible lower dimensional irreps for the not contracted lines. Is there an intelligent way to reduce the number of possible contractions. 2) I use the general method to construct the Young Projectors described in section 9.4. Yet in chapter 10 you use the symmetric projection operators from figure 9.1. This has the advantage that the final projection operators are symmetric (hermitian). Is there also a general algorithm to construct these Young Projectors from figure 9.1?