A339248 List of dimensions for which there exist several non-isomorphic irreducible representations of G2.

77, 2079, 4928, 30107, 56133, 133056, 315392, 812889, 1203125, 1515591, 1926848, 3592512, 8515584, 9058973, 20185088, 21948003, 32484375, 40920957, 52024896, 77000000, 96997824, 123318272, 136410197, 229920768, 244592271, 342513171, 371664293, 470421875

Offset: 1

Author

Andy Huchala, Nov 28 2020

Keywords

• nonn

Comments

Terms which could be repeated in A104599.

There are infinitely many terms in this sequence as the dimension formula is homogeneous of degree 6; see A181746.

Examples

			With the fundamental weights numbered as in Bourbaki, the highest weights 3,0 and 0,2 both correspond to irreducible representations of dimension 77. The highest weights 2,3 and 8,0 both correspond to irreducible representations of dimension 2079.
		

References

• N. Bourbaki, Lie Groups and Lie Algebras, Chapters 4-6, Springer, 1968, 231-233.

Links

• Andy Huchala, Table of n, a(n) for n = 1..20000
• Andy Huchala, C++ program
• Wikipedia, G2 (mathematics)

Crossrefs

Cf. A181746, A104599.

Formula

Given a vector of 2 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.