Search: id:A121214
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%I A121214
%S A121214 1,4,6,10,15,20,35,36,45,50,56,60,64,70,84,105,120,126,140,160,165,175,
%T A121214 189,196,216,220,224,256,270,280,286,300,315,336,360,364,384,396,420,
%U A121214 440,455,480,500,504,540,560,594,616,630,640,680,715,729,735,750,756
%N A121214 Dimensions of the irreducible representations of the algebraic group 
               SL4 (equivalently, simple Lie algebra of type A3) over the complex 
               numbers, listed in increasing order.
%C A121214 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 A121214 N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, Springer, 2002.
%D A121214 J. E. Humphreys, Introduction to Lie algebras and representation theory, 
               Springer, 1997.
%H A121214 <a href="http://en.wikipedia.org/wiki/Special_linear_group">Wikipedia 
               article</a> on the special linear group
%F A121214 Given a vector of 3 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 A121214 The highest weight 000 corresponds to the 1-dimensional module on which 
               SL4 acts trivially. The standard representation and its dual have 
               dimension 4 (the second term in the sequence) and highest weights 
               100 and 001. The third term in the sequence, 6, is the dimension 
               of the representation of SL4 on the second exterior power of the 
               standard representation; it has highest weight 010. The fourth term, 
               10, is the dimension of the second symmetric power of the standard 
               representation or its dual, with highest weight 200 or 002. The fifth 
               term, 15, corresponds to the adjoint representation with highest 
               weight 101.
%o A121214 (GAP) # see program at A121732
%Y A121214 Cf. A121732, A121741.
%Y A121214 Sequence in context: A084372 A140611 A076957 this_sequence A116996 A004399 
               A028282
%Y A121214 Adjacent sequences: A121211 A121212 A121213 this_sequence A121215 A121216 
               A121217
%K A121214 nonn
%O A121214 1,2
%A A121214 Skip Garibaldi (skip(AT)member.ams.org), Aug 20 2006

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