login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A129068 A128894[n,k] for k=1 : Coxeter numbers as defined by Bulgadaev for exceptional group sequence using critical exponent solution. 0
2, 3, 3, 6, 9, 12, 18, 24, 30, 50 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

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 two-dimensional systems with internal symmetries, arXiv:hep-th/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

AUTHOR

Roger L. Bagula, May 11 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 2 13:03 EST 2016. Contains 278678 sequences.