A339249 List of dimensions for which there exist several non-isomorphic irreducible representations of F4.

1053, 160056, 4313088, 28481544, 655589376, 17666408448, 30011240259, 116660404224, 168658209720, 257425688520, 2585493646164, 2685294084096, 7548492087864, 9283085543160, 9283085543160, 32912757834840, 62027889765660, 72361609003008, 81736097625000

Offset

1,1

Comments

Terms in this sequence are the terms which could be repeated in A121738.

This sequence is infinitely long; see A181746.

References

N. Bourbaki, Lie Groups and Lie Algebras, Chapters 4-6, Springer, 1968, 223-224.

Links

Andy Huchala, Table of n, a(n) for n = 1..804

Andy Huchala, C++ program

Formula

Given a vector of 4 nonnegative integers, the Weyl dimension formula tells you the dimension of the corresponding irreducible representation. The list of such dimensions is then sorted numerically and duplicates recorded.

Example

With the fundamental weights numbered as in Bourbaki, the highest weights 1001 and 2000 both correspond to irreducible representations of dimension 1053. The highest weights 0102 and 2002 both correspond to irreducible representations of dimension 160056.

Crossrefs

Cf. A121738, A181746.

Sequence in context: A191858 A353054 A090005 * A359624 A225714 A158692

Adjacent sequences: A339246 A339247 A339248 * A339250 A339251 A339252

Keyword

nonn

Author

Andy Huchala, Nov 28 2020

Status

approved