%I A121732
%S A121732 1,248,3875,27000,30380,147250,779247,1763125,2450240,4096000,4881384,
%T A121732 6696000,26411008,70680000,76271625,79143000,146325270,203205000,
%U A121732 281545875,301694976,344452500,820260000,1094951000,2172667860
%N A121732 Dimensions of the irreducible representations of the simple Lie algebra 
               of type E8 over the complex numbers, listed in increasing order.
%C A121732 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.
%C A121732 Inequivalent representations can have the same dimension. For example, 
               the highest weights 10100000 and 10000011 (with fundamental weights 
               numbered as in Bourbaki) both correspond to irreducible representations 
               of dimension 8634368000.
%D A121732 J. E. Humphreys, Introduction to Lie algebras and representation theory, 
               Springer, 1997.
%H A121732 Skip Garibaldi, <a href="a121732.txt">Gap program</a>
%H A121732 Wikipedia, <a href="http://en.wikipedia.org/wiki/E8_%28mathematics%29">
               Article on e_8</a>
%F A121732 Given a vector of 8 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 A121732 The highest weight 00000000 corresponds to the 1-dimensional module on 
               which E8 acts trivially. The smallest faithful representation of 
               E8 is the adjoint representation of dimension 248 (the second term 
               in the sequence), with highest weight 00000001. The smallest non-fundamental 
               representation has dimension 27000 (the fourth term), corresponding 
               to the highest weight 00000002.
%o A121732 (GAP) # see program given in link.
%Y A121732 Cf. A121736, A121737, A121738, A121739, A104599, A121741, A121214, A030650.
%Y A121732 Sequence in context: A109478 A033554 A109476 this_sequence A028525 A135046 
               A027654
%Y A121732 Adjacent sequences: A121729 A121730 A121731 this_sequence A121733 A121734 
               A121735
%K A121732 nonn
%O A121732 1,2
%A A121732 Skip Garibaldi (skip(AT)mathcs.emory.edu), Aug 18 2006