%I A121738
%S A121738 1,26,52,273,324,1053,1274,2652,4096,8424,10829,12376,16302,17901,19278,
%T A121738 19448,29172,34749,76076,81081,100776,106496,107406,119119,160056,
%U A121738 184756,205751,212992,226746,340119,342056,379848,412776,420147,627912
%N A121738 Dimensions of the irreducible representations of the simple Lie algebra 
               of type F4 over the complex numbers, listed in increasing order.
%C A121738 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 A121738 N. Bourbaki, Lie groups and Lie algebras, Chapter 4-6, Springer, 2002.
%D A121738 J. E. Humphreys, Introduction to Lie algebras and representation theory, 
               Springer, 1997.
%H A121738 <a href="http://en.wikipedia.org/wiki/F4_%28mathematics%29">Wikipedia 
               article</a> on F<sub>4</sub>
%F A121738 Given a vector of 4 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 A121738 The highest weight 0000 corresponds to the 1-dimensional module on which 
               F4 acts trivially. The smallest faithful representation of F4 is 
               the "standard" representation of dimension 26 (the second term in 
               the sequence), with highest weight 0001. (This representation is 
               typically viewed as the trace zero elements in a 27-dimensional exceptional 
               Jordan algebra.) The adjoint representation has dimension 52 (the 
               third term in the sequence) and highest weight 1000.
%o A121738 (GAP) # see program at A121732
%Y A121738 Cf. A121732, A121736, A121737, A121739, A104599, A121741.
%Y A121738 Sequence in context: A158060 A122999 A040650 this_sequence A043331 A023701 
               A031459
%Y A121738 Adjacent sequences: A121735 A121736 A121737 this_sequence A121739 A121740 
               A121741
%K A121738 nonn
%O A121738 1,2
%A A121738 Skip Garibaldi (skip(AT)member.ams.org), Aug 19 2006