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

Author

Andy Huchala, Nov 28 2020

Keywords

• nonn

Comments

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

This sequence is infinitely long; see A181746.

Examples

			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.
		

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

Crossrefs

Cf. A121738, A181746.

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.