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A129520 Limited sequence of symmetric groups associate with the exceptional group sequence: as G2,F4,E6,E7,E7.5,E8,E9 ( or better? E11) as A3,S3,A4,S5,"? ",A5,S5. +0
1
3, 6, 24, 40, 60, 120 (list; graph; listen)
OFFSET

1,1

COMMENT

The calculation by hand based on dimensions of: Dim_Ex(i)-n(i)*Dim_Symm(i)=small_integer The groups E7.5 and E9 are better thought of as E7.6 and E11 when integer results are wanted. The "?" question mark group is a symmetrical group between s4 and A5 with dimension 40; it isn't in any of the books I have or on the web as far as I can find by searching. I'm not an Hecke algebra expert either.

REFERENCES

Gareth Jones and David Singerman, Bull. London Math Soc. 28, (1996) pages 561-590 ( A4,S4,A5 on p585)

EXAMPLE

14-4*3=2

52-8*6=4

78-5*12=6

133-5*24=13

190-4.6*40=6

248-4*60=8

484-4*120=4

Example:

DimEx(E7.6)/Dim_cartan=190/7.6=25

DimEx(E11)/Dim_cartan=484/11=44

which fit in the sequence of the traditional exceptional groups A118889

as:3, 7, 13, 13, 19, 25, 31,44

CROSSREFS

Cf. A118889.

Sequence in context: A101738 A083525 A106213 this_sequence A047167 A054718 A109155

Adjacent sequences: A129517 A129518 A129519 this_sequence A129521 A129522 A129523

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 28 2007

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.


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