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

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

Offset: 1

Author

Andy Huchala, Apr 09 2021

Keywords

• nonn

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.

Examples

			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]
		

References

• N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, Springer, 2002.
• J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1997.

Links

• Andy Huchala, Table of n, a(n) for n = 1..12
• Andy Huchala, C++ Program

Crossrefs

Cf. A181746, A121737.

Programs

Java

// See A181746 and A121737.
(C++) // See A181746.