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A343266 List of dimensions for which there exist 8 or more non-isomorphic irreducible representations of E6. 1
7980534952482277785600, 81594430454916707328000, 14562708974765215732435968000, 548418186007940753739828795801600, 5607126565433818566044216721408000, 1000741740604516653587154703585640448000, 1197835483167781694195253526401026457600 (list; graph; refs; listen; history; text; internal format)
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

See A181746 and A121737.

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

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Last modified October 7 08:05 EDT 2022. Contains 357270 sequences. (Running on oeis4.)