

A343266


List of dimensions for which there exist 8 or more nonisomorphic irreducible representations of E6.


1



7980534952482277785600, 81594430454916707328000, 14562708974765215732435968000, 548418186007940753739828795801600, 5607126565433818566044216721408000, 1000741740604516653587154703585640448000, 1197835483167781694195253526401026457600
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OFFSET

1,1


COMMENTS

Terms which would appear in A121737 eight times or more if it included repeats.
There are infinitely many terms in this sequence; see A181746. For example, 548418186007940753739828795801600 = 2^36 * 7980534952482277785600, and additional dimensions may be obtained by replacing 2^36 with n^36 for any positive integer n.


REFERENCES

N. Bourbaki, Lie groups and Lie algebras, Chapters 46, Springer, 2002.
J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1997.


LINKS



EXAMPLE

With fundamental weights as ordered in Bourbaki, the eight irreducible E6 representations with dimension 7980534952482277785600 have highest weights as follows:
[ 1, 5, 2, 5, 0, 7]
[ 7, 5, 0, 5, 2, 1]
[ 5, 7, 2, 3, 2, 1]
[ 1, 7, 2, 3, 2, 5]
[ 1, 5, 6, 1, 0,11]
[11, 5, 0, 1, 6, 1]
[ 4, 5, 3, 1, 0,14]
[14, 5, 0, 1, 3, 4]


PROG



CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



