A339251 List of dimensions for which there exist several non-isomorphic irreducible representations of E7.

1903725824, 16349520330, 8971740610560, 34695403142400, 824608512000000, 4660749155462400, 5099341625414400, 6681177699123200, 35516286743137200, 61732518862014000, 95583619816439040, 631645584845184000, 972524604841574400, 1199167756428096000

Offset: 1

Author

Andy Huchala, Apr 02 2021

Keywords

• nonn

Comments

Terms which could be repeated in A121736.

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

Examples

			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.
		

References

• N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, Springer, 2002.
• J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1997.

Links

• Andy Huchala, Table of n, a(n) for n = 1..9000
• Andy Huchala, C++ Program
• Wikipedia, E7 (mathematics)

Crossrefs

Cf. A181746, A121736.

Programs

Java

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