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

Abstract: It is shown that in the presence of a nonvanishing cosmological constant, Strominger's infinite-dimensional $\mathrm{w_{1+\infty}}$ 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 $\mathrm{w{1+\infty}}$ are also discussed.