# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a104599 Showing 1-1 of 1 %I A104599 #12 Nov 22 2020 03:24:55 %S A104599 1,7,14,27,64,77,182,189,273,286,378,448,714,729,748,896,924,1254, %T A104599 1547,1728,1729,2079,2261,2926,3003,3289,3542,4096,4914,4928,5005, %U A104599 5103,6630,7293,7371,7722,8372,9177,9660,10206,10556,11571,11648,12096,13090 %N A104599 Dimensions of the irreducible representations of the simple Lie algebra of type G2 over the complex numbers, listed in increasing order. %C A104599 We include "1" for the 1-dimensional trivial representation and we list each dimension once, ignoring the possibility that inequivalent representations may have the same dimension. %D A104599 N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, Springer, 2002. %D A104599 J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1997. %H A104599 Andy Huchala, Table of n, a(n) for n = 1..20000 %H A104599 Andy Huchala, Java program %H A104599 Wikipedia, G_2 (mathematics) %F A104599 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. %e A104599 The highest weight 00 corresponds to the 1-dimensional module on which G2 acts trivially. The smallest faithful representation of G2 is the "standard" representation of dimension 7 (the second term in the sequence), with highest weight 10. (This vector space can be viewed as the trace zero elements of an octonion algebra.) The third term in the sequence, 14, is the dimension of the adjoint representation, which has highest weight 01. %o A104599 (GAP) # see program at sequence A121732 %Y A104599 Cf. A121732, A121736, A121737, A121738, A121739. %K A104599 nonn %O A104599 1,2 %A A104599 Skip Garibaldi (skip(AT)member.ams.org), Aug 19 2006 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE