w(1+infinity) Algebra with a Cosmological Constant and the Celestial Sphere

It is shown that in the presence of a nonvanishing cosmological constant, Strominger’s infinite-dimensional ${\mathrm{w}}_{1+\mathrm{\infty }}$ algebra of soft graviton symmetries is modified in a simple way. The deformed algebra contains a subalgebra generating $SO(1,4)$ or $SO(2,3)$ symmetry groups of ${\text{dS}}_4$ or ${\text{AdS}}_4$, depending on the sign of the cosmological constant. The transformation properties of soft gauge symmetry currents under the deformed ${\mathrm{w}}_{1+\mathrm{\infty }}$ are also discussed.