Spherical Harmonics Ylm(θ,ϕ): Positive and Negative Integer Representations of su(1,1) for l-m and l+m by H. Fakhri

“…The azimuthal and magnetic quantum numbers of spherical harmonics Ylm(θ,ϕ) describe quantization corresponding to the magnitude and z-component of angular momentum operator in the framework of realization of su(2) Lie algebra symmetry. The azimuthal quantum number l allocates to itself an additional ladder symmetry by the operators which are written in terms of l. …”
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