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Search: id:A129068
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| A129068 |
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A128894[n,k] for k=1 : Coxeter numbers as defined by Bulgadaev for exceptional group sequence using critical exponent solution. |
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OFFSET
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1,1
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COMMENT
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The building exceptional group symmetry sequence in Cartan notation is ( Deligne-Landsberg): {A1,A2,G2,D4,F4,E6,E7,E7.5,E8,E9} The Coxeter number seem to be related to the total powers in the elliptical invariants for exceptional groups. I have used 2/11 for the F4 critical exponent instead of Bulgadaev's 1/4 because 2/11 fits the linearity of the groups better.
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REFERENCES
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S. A. Bulgadaev, arXiv : hep - th/9906091v1 12 Jun 1999 http : // arXiv.org/pdf/hep - th/9906091
J. M. Landsberg, The sextonions and E_{7 1/2} (with L.Manivel) (Advances in Math 201(2006) p143 - 179) page 22
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FORMULA
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Criticalexponent=k/(k+hg)={2/(1 + 3), 2/(2 + 3), 2/5, 1/4, 2/11, 1/7, 1/10, 1/13, 1/16, 1/26}; hg=Coxeter number=(number of roots)/(rank of group) hg = Flatten[Table[x /. Solve[2/(2 + x) - b[[n]] == 0, x], {n, 1, Length[b]}]]
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MATHEMATICA
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(*S.A Bulgadaev, arXiv : hep - th/9906091v1 12 Jun 1999*) (*http : // arXiv.org/pdf/hep - th/9906091*) b = {2/(1 + 3), 2/(2 + 3), 2/5, 1/4, 2/11, 1/7, 1/10, 1/13, 1/16, 1/26}; hg = Flatten[Table[x /. Solve[2/(2 + x) - b[[n]] == 0, x], {n, 1, Length[b]}]]
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CROSSREFS
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Cf. A128894, A109161, A129024, A129025.
Sequence in context: A027100 A060840 A074717 this_sequence A079888 A165257 A059191
Adjacent sequences: A129065 A129066 A129067 this_sequence A129069 A129070 A129071
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 11 2007
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