Next highest weight and other lower $SU(3)$ irreducible representations with proxy-$SU(4)$ symmetry for nuclei with 32 ≤ Z,N ≤ 46

In the applications of proxy-SU(3) model in the context of determining $(β,γ)$ values for nuclei across the periodic table, for understanding the preponderance of triaxial shapes in nuclei with Z ≥ 30, it is seen that one needs not only the highest weight (hw) or leading $SU(3)$ irreducible representation (irrep) (λH, μH) but also the lower $SU(3)$ irreps $(λ,μ)$ such that 2λ+ μ=2λH + μH-3r with $r=0,1$ and $2$ [Bonatsos et al., Symmetry { 16}, 1625 (2024)]. These give the next highest weight (nhw) irrep, next-to-next highest irrep (nnhw) and so on. Recently, it is shown that for nuclei with 32 ≤ Z,N ≤ 46, there will be not only proxy-$SU(3)$ but also proxy-$SU(4)$ symmetry [Kota and Sahu, Physica Scripta { 99}, 065306 (2024)]. Following these developments, presented in this paper are the $SU(3)$ irreps $(λ,μ)$ with 2λ+ μ=2λH + μH-3r, $r=0,1,2$ for various isotopes of Ge, Se, Kr, Sr, Zr, Mo, Ru and Pd (with 32 ≤ N ≤ 46) assuming good proxy-$SU(4)$ symmetry. A simple method for obtaining the SU(3) irreps is described and applied. The tabulations for proxy-$SU(3)$ irreps provided in this paper will be useful in further investigations of triaxial shapes in these nuclei.