OFFSET
1,2
COMMENTS
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.
REFERENCES
N. Bourbaki, Lie groups and Lie algebras, Chapter 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..20000
Andy Huchala, Java program
Wikipedia, F_4 (mathematics)
FORMULA
Given a vector of 4 nonnegative integers, the Weyl dimension formula tells you the dimension of the corresponding irreducible representation. The list of such dimensions is then sorted numerically.
EXAMPLE
The highest weight 0000 corresponds to the 1-dimensional module on which F4 acts trivially. The smallest faithful representation of F4 is the "standard" representation of dimension 26 (the second term in the sequence), with highest weight 0001. (This representation is typically viewed as the trace zero elements in a 27-dimensional exceptional Jordan algebra.) The adjoint representation has dimension 52 (the third term in the sequence) and highest weight 1000.
PROG
(GAP) # see program at A121732
CROSSREFS
KEYWORD
nonn
AUTHOR
Skip Garibaldi (skip(AT)member.ams.org), Aug 19 2006
STATUS
approved