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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified January 23 03:15 EST 2022. Contains 350504 sequences. (Running on oeis4.)