

A129068


A128894[n,k] for k=1 : Coxeter numbers as defined by Bulgadaev for exceptional group sequence using critical exponent solution.


0




OFFSET

1,1


COMMENTS

The building exceptional group symmetry sequence in Cartan notation is ( DeligneLandsberg): {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.


REFERENCES

J. M. Landsberg, The sextonions and E_{7 1/2} (with L.Manivel) (Advances in Math 201(2006) p143  179) page 22


LINKS

Table of n, a(n) for n=1..10.
S. A. Bulgadaev, BKT phase transition in twodimensional systems with internal symmetries, arXiv:hepth/9906091 (1999).


FORMULA

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]}]]


MATHEMATICA

(*S.A Bulgadaev, arXiv : hep  th/9906091v1 12 Jun 1999*) 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]}]]


CROSSREFS

Cf. A128894, A109161, A129024, A129025.
Sequence in context: A060840 A074717 A218137 * A079888 A165257 A059191
Adjacent sequences: A129065 A129066 A129067 * A129069 A129070 A129071


KEYWORD

nonn,fini,full,uned,changed


AUTHOR

Roger L. Bagula, May 11 2007


STATUS

approved



