

A129520


Orders of symmetric groups associated with the exceptional groups G2, F4, E6, E7, E7.5, E8, E9 (or better? E11): A_3, S_3, A_4, S_5, "? ", A_5, S_5.


0




OFFSET

1,1


COMMENTS

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 is not in any of the books I have or on the web as far as I can find by searching.


REFERENCES

Gareth Jones and David Singerman, Bull. London Math Soc. 28, (1996) pages 561590 ( A_4, S_4, A_5 on p585)


LINKS



EXAMPLE

144*3=2
528*6=4
785*12=6
1335*24=13
1904.6*40=6
2484*60=8
4844*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



KEYWORD

nonn,uned,obsc


AUTHOR



EXTENSIONS



STATUS

approved



