From Jutho.Haegeman Mar 3 2008 Subject: Re: so(n) 3-j and 6-j coefficients I'm very interested in better (and faster) ways to calculate the 3-j and 6-j coefficients. Does your implementation also works for spinorial irreps? How slow/fast does it work? And what language is it written in? My implementation is written in Matlab. It does work for general O(n). For doing symbolical calculations, Matlab communicates with Maple, which has another negative influence on the overall speed. Fixing to a specific n-value makes my code faster, yet the scaling to higher weight irreps still remains and is of course the most terrible aspect of the code. I have two questions concerning the non-unitarity of the projectors: Does the remark of Georges Bergdolt about the non-orthogonality (due to the non-unitarity) of the Young projectors pose a problem? I start with a U(n)/GL(n) Young projector, and then project out all possible traces, starting with the highest number of contractions, and combining these with all possible Young projectors for the free lines. (I reasoned that using the Young projector or the real O(N) projector for the free lines doesn't matter, as all higher number of contractions are already projected out.) I still have to write the code to calculate the 3-j and 6-j coefficients. I first have to think trough which coefficients I'd really need. I guess the major lines will be parallel with the approach for U(n). Yet some possible difficulty already came to mind. In a U(n) Clebsch-Gordan series, you always end up with irrep with a total number of boxes (in the Young diagram) equal to the sum of the boxes of the two composing irreps. So the Clebsch-Gordan birdtrack just consists of the three projectors tied up in the correct order. In a O(N) Clebsch-Gordan series, the number of boxes can decrease (due to contractions). How then do you know which lines to contract? Probably this information is in the Littlewood-rule. It uses S-functions, which I do not know. And are such Clebsch-Gordan coefficients, constructed from non-unitary projectors, unitary? Probably not. How then to construct the complete projector, is it just P1 P1 P P2 P2 summed over all the irreps (with projector P) in the decomposition, with added contractions for irreps with a lesser number of boxes? ----------------------------