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

1,1

Comments

Terms which could be repeated in A121736.

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

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)

Example

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.

Prog

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

Crossrefs

Cf. A181746, A121736.

Sequence in context: A204813 A103752 A105383 * A233002 A165075 A034252

Adjacent sequences: A339248 A339249 A339250 * A339252 A339253 A339254

Keyword

nonn

Author

Andy Huchala, Apr 02 2021

Status

approved