%I A121736
%S A121736 1,56,133,912,1463,1539,6480,7371,8645,24320,27664,40755,51072,86184,
%T A121736 150822,152152,238602,253935,293930,320112,362880,365750,573440,617253,
%U A121736 861840,885248,915705,980343,2273920,2282280,2785552,3424256,3635840
%N A121736 Dimensions of the irreducible representations of the simple Lie algebra 
               of type E7 over the complex numbers, listed in increasing order.
%C A121736 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 A121736 See also comments in A030649.
%D A121736 N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, Springer, 2002.
%D A121736 J. E. Humphreys, Introduction to Lie algebras and representation theory, 
               Springer, 1997.
%H A121736 Skip Garibaldi, <a href="b121736.txt">Table of n, a(n) for n = 1..2856</
               a>
%H A121736 <a href="http://en.wikipedia.org/wiki/E7_%28mathematics%29">Wikipedia 
               article</a> on E<sub>7</sub>
%F A121736 Given a vector of 7 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 A121736 The highest weight 0000000 corresponds to the 1-dimensional module on 
               which E7 acts trivially. The smallest faithful representation of 
               E7 is the so-called "standard" representation of dimension 56 (the 
               second term in the sequence), with highest weight 0000001; it is 
               minuscule and supports the famous invariant quartic form. The adjoint 
               representation of dimension 133 (the third term in the sequence), 
               has highest weight 1000000.
%o A121736 (GAP) # see program given in sequence A121732
%Y A121736 Cf. A121732, A121737, A121738, A121739, A104599, A121741.
%Y A121736 Cf. A030649.
%Y A121736 Sequence in context: A030443 A135803 A048452 this_sequence A107937 A044307 
               A044688
%Y A121736 Adjacent sequences: A121733 A121734 A121735 this_sequence A121737 A121738 
               A121739
%K A121736 nonn
%O A121736 1,2
%A A121736 Skip Garibaldi (skip(AT)member.ams.org), Aug 18 2006