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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.

%I A121214 #9 Nov 27 2020 11:22:45
%S A121214 1,4,6,10,15,20,35,36,45,50,56,60,64,70,84,105,120,126,140,160,165,
%T A121214 175,189,196,216,220,224,256,270,280,286,300,315,336,360,364,384,396,
%U A121214 420,440,455,480,500,504,540,560,594,616,630,640,680,715,729,735,750,756
%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 Andy Huchala, <a href="/A121214/b121214.txt">Table of n, a(n) for n = 1..20000</a>
%H A121214 Andy Huchala, <a href="/A121214/a121214.java.txt">Java program</a>
%H A121214 Wikipedia, <a href="http://en.wikipedia.org/wiki/Special_linear_group">Special linear group</a>
%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.
%K A121214 nonn
%O A121214 1,2
%A A121214 Skip Garibaldi (skip(AT)member.ams.org), Aug 20 2006