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Alternative to the embedding formalism, we provide a group theoretic approachto the conformal primary basis for the massless field with arbitrary helicity.To this end, we first point out that $sl(2,\mathds{C})$ isometry gets enhancedto $sl(2,\mathds{C})\times D$ symmetry for the solution space of the masslessfield with arbitrary helicity. Then associated with $sl(2,\mathds{C})\times D$symmetry, we introduce the novel quadratic Casimirs and relevant tensor/spinorfields to derive 2 explicit constraints on the bulk dilatation and$sl(2,\mathds{C})$ Casimirs. With this, we further argue that the candidateconformal primary basis can be constructed out of the infinite tower of thedescendants of the left and right highest (lowest) conformal primarywavefunction of $sl(2,\mathds{C})$ Lie algebra, and the corresponding celestialconformal weights are determined by the bulk scaling dimension through solvingout the exact on-shell conformal primary wavefunctions, where on top of the twokinds of familiar-looking on-shell conformal primary wavefunctions, we alsoobtain another set of independent on-shell conformal primary wavefunctions forthe massless field with helicity $|s|\ge 1$. In passing, we also develop therelationship between the 4D Lorentz Lie algebra and 2D conformal Lie algebrafrom scratch, and present an explicit derivation for the two importantproperties associated with the conformal primary wavefunctions.

$sl(2,\mathds{C})\times D$ symmetry and conformal primary basis for massless fields