cp's OEIS Frontend

A343266 List of dimensions for which there exist 8 or more non-isomorphic irreducible representations of E6.

%I A343266 #22 Jun 02 2024 11:04:05
%S A343266 7980534952482277785600,81594430454916707328000,
%T A343266 14562708974765215732435968000,548418186007940753739828795801600,
%U A343266 5607126565433818566044216721408000,1000741740604516653587154703585640448000,1197835483167781694195253526401026457600
%N A343266 List of dimensions for which there exist 8 or more non-isomorphic irreducible representations of E6.
%C A343266 Terms which would appear in A121737 eight times or more if it included repeats.
%C A343266 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 A343266 N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, Springer, 2002.
%D A343266 J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1997.
%H A343266 Andy Huchala, <a href="/A343266/b343266.txt">Table of n, a(n) for n = 1..12</a>
%H A343266 Andy Huchala, <a href="/A343266/a343266.cpp.txt">C++ Program</a>
%e A343266 With fundamental weights as ordered in Bourbaki, the eight irreducible E6 representations with dimension 7980534952482277785600 have highest weights as follows:
%e A343266   [ 1, 5, 2, 5, 0, 7]
%e A343266   [ 7, 5, 0, 5, 2, 1]
%e A343266   [ 5, 7, 2, 3, 2, 1]
%e A343266   [ 1, 7, 2, 3, 2, 5]
%e A343266   [ 1, 5, 6, 1, 0,11]
%e A343266   [11, 5, 0, 1, 6, 1]
%e A343266   [ 4, 5, 3, 1, 0,14]
%e A343266   [14, 5, 0, 1, 3, 4]
%o A343266 (Java) // See A181746 and A121737.
%o A343266 (C++) // See A181746.
%Y A343266 Cf. A181746, A121737.
%K A343266 nonn
%O A343266 1,1
%A A343266 _Andy Huchala_, Apr 09 2021