%I A121739
%S A121739 1,8,28,35,56,112,160,224,294,300,350,567,672,840,1296,1386,1400,1568,
%T A121739 1680,1925,2400,2640,2800,3675,3696,4096,4312,4536,4719,5775,6160,6600,
%U A121739 7392,7776,7840,8008,8800,8910,8918,10752,12320,12936,13013,13728,15015
%N A121739 Dimensions of the irreducible representations of the simple Lie algebra
of type D4 over the complex numbers, listed in increasing order.
%C A121739 We include "1" for the 1-dimensional trivial representation and we list
each dimension once, ignoring the fact that inequivalent representations
may have the same dimension.
%D A121739 N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, Springer, 2002.
%D A121739 J. E. Humphreys, Introduction to Lie algebras and representation theory,
Springer, 1997.
%H A121739 <a href="http://en.wikipedia.org/wiki/Triality">Wikipedia article</a>
on triality
%F A121739 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 A121739 The highest weight 0000 corresponds to the 1-dimensional module on which
D4 acts trivially. The second second term in the sequence is 8, corresponding
to the three inequivalent representations with highest weights 1000,
0010 and 0001 respectively. The third term in the sequence is 28,
corresponding to the adjoint representation, which has highest weight
0100.
%o A121739 (GAP) # see program at sequence A121732
%Y A121739 Cf. A121732, A121736, A121737, A121738, A104599.
%Y A121739 Sequence in context: A053619 A112663 A006377 this_sequence A166729 A131850
A009504
%Y A121739 Adjacent sequences: A121736 A121737 A121738 this_sequence A121740 A121741
A121742
%K A121739 nonn
%O A121739 1,2
%A A121739 Skip Garibaldi (skip(AT)member.ams.org), Aug 19 2006
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