%I #22 May 31 2024 14:50:45

%S 1903725824,16349520330,8971740610560,34695403142400,824608512000000,

%T 4660749155462400,5099341625414400,6681177699123200,35516286743137200,

%U 61732518862014000,95583619816439040,631645584845184000,972524604841574400,1199167756428096000

%N List of dimensions for which there exist several non-isomorphic irreducible representations of E7.

%C Terms which could be repeated in A121736.

%C There are infinitely many terms in this sequence; see A181746.

%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="/A339251/b339251.txt">Table of n, a(n) for n = 1..9000</a>

%H Andy Huchala, <a href="/A339251/a339251.cpp.txt">C++ Program</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/E7_(mathematics)">E7 (mathematics)</a>

%e With the fundamental weights numbered as in Bourbaki, the irreducible E7-modules with highest weights [0,0,0,1,1,0,0] and [0,0,0,0,0,2,3] both have dimension 1903725824. The highest weights [3,0,0,1,0,0,0] and [0,0,0,0,1,0,5] both correspond to irreducible representations of dimension 16349520330.

%o (Java) // See Links section of A181746.

%o (C++) // See Links section above and in A181746.

%Y Cf. A181746, A121736.

%K nonn

%O 1,1

%A _Andy Huchala_, Apr 02 2021