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

1,1

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 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

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

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

Crossrefs

Cf. A181746, A121737.

Sequence in context: A076335 A280301 A115542 * A330009 A171265 A353185

Adjacent sequences: A343263 A343264 A343265 * A343267 A343268 A343269

Keyword

nonn

Author

Andy Huchala, Apr 09 2021

Status

approved