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A121732 Dimensions of the irreducible representations of the simple Lie algebra of type E8 over the complex numbers, listed in increasing order.

%I A121732 #15 Nov 22 2020 01:29:07
%S A121732 1,248,3875,27000,30380,147250,779247,1763125,2450240,4096000,4881384,
%T A121732 6696000,26411008,70680000,76271625,79143000,146325270,203205000,
%U A121732 281545875,301694976,344452500,820260000,1094951000,2172667860
%N A121732 Dimensions of the irreducible representations of the simple Lie algebra of type E8 over the complex numbers, listed in increasing order.
%C A121732 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 A121732 Inequivalent representations can have the same dimension. For example, the highest weights 10100000 and 10000011 (with fundamental weights numbered as in Bourbaki) both correspond to irreducible representations of dimension 8634368000.
%D A121732 J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1997.
%H A121732 Andy Huchala, <a href="/A121732/b121732.txt">Table of n, a(n) for n = 1..20000</a>
%H A121732 Skip Garibaldi, <a href="/A121732/a121732.txt">Gap program</a>
%H A121732 Wikipedia, <a href="https://en.wikipedia.org/wiki/E8_%28mathematics%29">E8 (mathematics)</a>
%F A121732 Given a vector of 8 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 A121732 The highest weight 00000000 corresponds to the 1-dimensional module on which E8 acts trivially. The smallest faithful representation of E8 is the adjoint representation of dimension 248 (the second term in the sequence), with highest weight 00000001. The smallest non-fundamental representation has dimension 27000 (the fourth term), corresponding to the highest weight 00000002.
%o A121732 (GAP) # see program given in link.
%Y A121732 Cf. A121736, A121737, A121738, A121739, A104599, A121741, A121214, A030650.
%K A121732 nonn
%O A121732 1,2
%A A121732 Skip Garibaldi (skip(AT)mathcs.emory.edu), Aug 18 2006