Search: id:A121737
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%I A121737
%S A121737 1,27,78,351,650,1728,2430,2925,3003,5824,7371,7722,17550,19305,34398,
%T A121737 34749,43758,46332,51975,54054,61425,70070,78975,85293,100386,105600,
%U A121737 112320,146432,252252,314496,359424,371800,386100,393822,412776,442442
%N A121737 Dimensions of the irreducible representations of the simple Lie algebra 
               of type E6 over the complex numbers, listed in increasing order.
%C A121737 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 A121737 N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, Springer, 2002.
%D A121737 J. E. Humphreys, Introduction to Lie algebras and representation theory, 
               Springer, 1997.
%H A121737 <a href="http://en.wikipedia.org/wiki/E6_%28mathematics%29">Wikipedia 
               article</a> on E<sub>6</sub>
%F A121737 Given a vector of 6 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 A121737 The highest weight 000000 corresponds to the 1-dimensional module on 
               which E6 acts trivially. The smallest faithful representations of 
               E6 have dimension 27, highest weight 000001 or 100000 and are minuscule. 
               The adjoint representation of dimension 78 (the third term in the 
               sequence) has highest weight 010000.
%o A121737 (GAP) # see program at sequence A121732
%Y A121737 Cf. A121732, A121736, A121738, A121739, A104599, A121741.
%Y A121737 Sequence in context: A163506 A044165 A044546 this_sequence A124726 A126381 
               A129254
%Y A121737 Adjacent sequences: A121734 A121735 A121736 this_sequence A121738 A121739 
               A121740
%K A121737 nonn
%O A121737 1,2
%A A121737 Skip Garibaldi (skip(AT)member.ams.org), Aug 19 2006

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