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Representations of the (Lorentz) conformal group with the soft operators ashighest weight vectors have two universal properties, which we clearly state inthis paper. Given a soft operator with a certain dimension and spin, the firstproperty is about the existence of "(large) gauge transformation" that acts onthe soft operator. The second property is the decoupling of (large)gauge-invariant null-states of the soft operators from the $S$-matrix elements.In each case, the decoupling equation has the form of zero field-strengthcondition with the soft operator as the (gauge) potential. Null-statedecoupling effectively reduces the number of polarisation states of the softparticle and is crucial in deriving soft-theorems from the Ward identities ofasymptotic symmetries. To the best of our understanding, these properties arenot directly related to the Lorentz invariance of the $S$-matrix or theexistence of asymptotic symmetries. We also verify that the results obtainedfrom the decoupling of null-states are consistent with the leading andsubleading soft-theorems with finite energy massive and massless particles inthe external legs.

Conformal properties of soft operators -- 2 : Use of null-states