A181746 List of dimensions for which there exist several non-isomorphic irreducible representations of E8.

8634368000, 175898504162692612600853299200000, 569584588357708246352221171200000000000, 30903356351561222538825891668691517440000, 75783579745006249731939558173442048000000, 221669803220344213547594484715842176665500, 11477043671509412495692698759458678235987968000

Offset: 1

Author

David A. Madore, Nov 08 2010

Keywords

• nonn

Comments

Terms in this sequence are the terms which are repeated in A121732.

This sequence is infinitely long. For example, there exists two non-isomorphic irreducible E8 representations of dimension n^120 * 8634368000 for any n>0 (the dimension formula is homogeneous of degree 120 after a suitable change of variables). I have found no dimension with more than two non-isomorphic irreducible E8 representations. - Andy Huchala, Nov 22 2020

Examples

			With the fundamental weights numbered as in Bourbaki, the highest weights 10100000 and 10000011 both correspond to irreducible representations of dimension 8634368000. The highest weights 23000130 and 12000231 both correspond to irreducible representations of dimension 175898504162692612600853299200000.
		

References

• N. Bourbaki, Lie Groups and Lie Algebras Chapters 4-6, Springer, 1968, 283-285.

Links

• Andy Huchala, Table of n, a(n) for n = 1..332
• Andy Huchala, Java program
• Andy Huchala, C++ program

Crossrefs

Cf. A121732.