%I A104599
%S A104599 1,7,14,27,64,77,182,189,273,286,378,448,714,729,748,896,924,1254,1547,
%T A104599 1728,1729,2079,2261,2926,3003,3289,3542,4096,4914,4928,5005,5103,6630,
%U A104599 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 <a href="http://en.wikipedia.org/wiki/G2_%28mathematics%29">Wikipedia 
               article</a> on G<sub>2</sub>
%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.
%Y A104599 Sequence in context: A025011 A030414 A095894 this_sequence A115874 A083495 
               A089644
%Y A104599 Adjacent sequences: A104596 A104597 A104598 this_sequence A104600 A104601 
               A104602
%K A104599 nonn
%O A104599 1,2
%A A104599 Skip Garibaldi (skip(AT)member.ams.org), Aug 19 2006