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%I #22 Apr 28 2021 02:44:21
%S 1,56,133,912,1463,1539,6480,7371,8645,24320,27664,40755,51072,86184,
%T 150822,152152,238602,253935,293930,320112,362880,365750,573440,
%U 617253,861840,885248,915705,980343,2273920,2282280,2785552,3424256,3635840
%N Dimensions of the irreducible representations of the simple Lie algebra of type E7 over the complex numbers, listed in increasing order.
%C 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 See also comments in A030649.
%D N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, Springer, 2002.
%D J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1997.
%H Andy Huchala, <a href="/A121736/b121736.txt">Table of n, a(n) for n = 1..20000</a> (terms 1..2856 from Skip Garibaldi)
%H Andy Huchala, <a href="/A121736/a121736.java.txt">Java program</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/E7_%28mathematics%29">E_7 (mathematics)</a>
%F Given a vector of 7 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 The highest weight 0000000 corresponds to the 1-dimensional module on which E7 acts trivially. The smallest faithful representation of E7 is the so-called "standard" representation of dimension 56 (the second term in the sequence), with highest weight 0000001; it is minuscule and supports the famous invariant quartic form. The adjoint representation of dimension 133 (the third term in the sequence), has highest weight 1000000.
%o (GAP) # see program given in sequence A121732
%Y Cf. A121732, A121737, A121738, A121739, A104599, A121741, A030649.
%K nonn
%O 1,2
%A Skip Garibaldi (skip(AT)member.ams.org), Aug 18 2006
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