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A339248
List of dimensions for which there exist several non-isomorphic irreducible representations of G2.
1
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, 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
Sequence in context: A073931 A296989 A105253 * A219126 A289232 A225703
KEYWORD
nonn
AUTHOR
Andy Huchala, Nov 28 2020
STATUS
approved