On Characters of F_4 Lie Algebra

TL;DR

This paper extends a previous method for computing irreducible characters of finite Lie algebras, specifically applying it to the more complex F_4 Lie algebra without using the Weyl character formula.

Contribution

It introduces an explicit method to determine irreducible characters for the F_4 Lie algebra, expanding on prior work that avoided the Weyl formula.

Findings

Successfully computed irreducible characters of F_4 Lie algebra

Extended previous methods from G_2 to F_4 case

Provided explicit character formulas for F_4

Abstract

In a previous work, we have given an explicit method to obtain irreducible characters of finite Lie algebras without referring to Weyl character formula. Irreducible characters of $G_2$ Lie algebra has been given as an example. The work is now extended to somewhat more complicated case of $F_4$ Lie algebra, in the same manner.