%I #19 Jun 03 2021 02:24:55
%S 7980534952482277785600,81594430454916707328000,
%T 14562708974765215732435968000,548418186007940753739828795801600,
%U 5607126565433818566044216721408000,1000741740604516653587154703585640448000,1197835483167781694195253526401026457600
%N List of dimensions for which there exist 8 or more nonisomorphic irreducible representations of E6.
%C Terms which would appear in A121737 eight times or more if it included repeats.
%C 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.
%D N. Bourbaki, Lie groups and Lie algebras, Chapters 46, Springer, 2002.
%D J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1997.
%H Andy Huchala, <a href="/A343266/b343266.txt">Table of n, a(n) for n = 1..12</a>
%H Andy Huchala, <a href="/A343266/a343266.cpp.txt">C++ Program</a>
%e With fundamental weights as ordered in Bourbaki, the eight irreducible E6 representations with dimension 7980534952482277785600 have highest weights as follows:
%e [ 1, 5, 2, 5, 0, 7]
%e [ 7, 5, 0, 5, 2, 1]
%e [ 5, 7, 2, 3, 2, 1]
%e [ 1, 7, 2, 3, 2, 5]
%e [ 1, 5, 6, 1, 0,11]
%e [11, 5, 0, 1, 6, 1]
%e [ 4, 5, 3, 1, 0,14]
%e [14, 5, 0, 1, 3, 4]
%o See A181746 and A121737.
%Y Cf. A181746, A121737.
%K nonn
%O 1,1
%A _Andy Huchala_, Apr 09 2021
