THE LIE ALGEBRA su(3) REPRESENTATION WITH RESPECT TO ITS BASIS

The eight-dimensional Lie algebra of 3×3 anti-Hermitian matrices withits traces equal to zero is denoted by su(3) whose Lie group is denoted by SU(3). Theresearch aims to provide all representations of su(3) with respect to its basis which isrealized on the three complex variables homogeneous polynomials P1 of degree three. The first step is to construct representations of SU(3) on the space H and the second step is to find all derived representations of SU(3). The obtained results are eight explicit formulas of representations su(3) ↷ P1.