11 Dec 2002, 7 Feb 2004 Bernard to Predrag emails summarized text: ------------------------------------------------- Your Magic Triangle is distinctly different from mine. The first occurence of my triangle is Nuffield workshop summer 1980, preprint fall 1980: B. L. Julia, ``Group disintegrations'', in S. Hawking and M. Rocek, eds. {\em Superspace and Supergravity} (Cambridge Univ. Press, Cambridge 1981) It was stimulated by a number of ideas, the remark by Gibbons and Hawking in 1979 on Gravitational instantons and Ehlers symmetry, the vague but provocating remarks of Morel and Thierry Mieg quoted in my paper. My version was was definitely not motivated by yours, the N=8 column is much older and the desire to understand the other N's came in order to fit in the N=1 or 0 case ie GR then to understand the E_9 or affine case which I had in mind since 1978. My first reference to your work is in the first paper of 1981 quoted above, about negative dimensions. As you confirm, your E_7 result was written up after my first paper with Cremmer. Your work is not related to mine as far as I can see even now; you have no real forms and the real forms that I have do not even match with the entire Tits-Freudenthal subsquare. The intersection of the two triangles is the [3x3] Magic Square which I knew long before those times and probably from similar sources, (I heard F. Gursey in a Princeton seminar on exceptional groups, about 1975). F_4 is a possibility for the Magic Square of Kugo Sierra and Townsend, but not G_2. Bernard L. Julia ENS-CNRS/LPT 24 rue Lhomond 75005 Paris FRANCE Tel. (01)47077146. FAX. (01)43367666. caius(at)lpt.ens.fr ------------------ references with Julia's triangle: ``Disintegration (i.e. Oxidation) for En Cosets'' E. Cremmer, B. Julia, H. Lu, C.N. Pope Higher-dimensional Origin of D=3 Coset Symmetries hep-th/9909099 Applied Math vol 21 (1985) 355. (I have not seen this one myself) Pierre Henry-Labordere, Bernard Julia, Louis Paulot Borcherds symmetries in M-theory JHEP 0204 (2002) 049 hep-th/0203070 B.L. Julia Magics of M-gravity Fortsch. Phys. 49 (2001) 551-555 hep-th/0105031