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A121738 Dimensions of the irreducible representations of the simple Lie algebra of type F4 over the complex numbers, listed in increasing order.

%I A121738 #8 Nov 22 2020 04:27:57
%S A121738 1,26,52,273,324,1053,1274,2652,4096,8424,10829,12376,16302,17901,
%T A121738 19278,19448,29172,34749,76076,81081,100776,106496,107406,119119,
%U A121738 160056,184756,205751,212992,226746,340119,342056,379848,412776,420147,627912
%N A121738 Dimensions of the irreducible representations of the simple Lie algebra of type F4 over the complex numbers, listed in increasing order.
%C A121738 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 A121738 N. Bourbaki, Lie groups and Lie algebras, Chapter 4-6, Springer, 2002.
%D A121738 J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1997.
%H A121738 Andy Huchala, <a href="/A121738/b121738.txt">Table of n, a(n) for n = 1..20000</a>
%H A121738 Andy Huchala, <a href="/A121738/a121738.java.txt">Java program</a>
%H A121738 Wikipedia, <a href="http://en.wikipedia.org/wiki/F4_%28mathematics%29">F_4 (mathematics)</a>
%F A121738 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 A121738 The highest weight 0000 corresponds to the 1-dimensional module on which F4 acts trivially. The smallest faithful representation of F4 is the "standard" representation of dimension 26 (the second term in the sequence), with highest weight 0001. (This representation is typically viewed as the trace zero elements in a 27-dimensional exceptional Jordan algebra.) The adjoint representation has dimension 52 (the third term in the sequence) and highest weight 1000.
%o A121738 (GAP) # see program at A121732
%Y A121738 Cf. A121732, A121736, A121737, A121739, A104599, A121741.
%K A121738 nonn
%O A121738 1,2
%A A121738 Skip Garibaldi (skip(AT)member.ams.org), Aug 19 2006