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

1,1

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.

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)

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.

Example

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.

Crossrefs

Cf. A181746, A104599.

Sequence in context: A073931 A296989 A105253 * A219126 A289232 A225703

Adjacent sequences: A339245 A339246 A339247 * A339249 A339250 A339251

Keyword

nonn

Author

Andy Huchala, Nov 28 2020

Status

approved