

A181746


List of dimensions for which there exist several nonisomorphic irreducible representations of E8.


6



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

1,1


COMMENTS

Terms in this sequence are the terms which are repeated in A121732.
This sequence is infinitely long. For example, there exists two nonisomorphic 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 nonisomorphic irreducible E8 representations.  Andy Huchala, Nov 22 2020


REFERENCES

N. Bourbaki, Lie Groups and Lie Algebras Chapters 46, Springer, 1968, 283285.


LINKS



EXAMPLE

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.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



