Mixed-helicity sector of celestial symmetries and the shadow transform

The asymptotic symmetries of null infinity in asymptotically flat spacetimes can be enhanced to a w1+∞ algebra, when restricting to a single graviton helicity sector. These symmetries were first extracted from the operator product expansion (OPE) of conformal gravitons in celestial holography. They later found a canonical realization in the bracket of an infinite set of higher-spin charges. Combining both helicity sectors in the full theory of gravity presents difficulties from both the canonical and the celestial perspective. In this talk, I will present a covariant phase space analysis of higher-spin gravitational charges and analyze their mixed-helicity bracket. I will show that, when one helicity is restricted to the wedge sector, the bracket reduces to a closed structure, where the shadow transform plays a key role. This framework also yields a dual-mass extension of the BMS algebra in the lower-spin sector. On the celestial side, I will use an existing bracket-OPE correspondence to provide a prescription for resolving the soft-limit ordering ambiguity in doubly-soft mixed-helicity OPEs, and furthermore to compute OPEs of shadow-transformed conformally soft gravitons directly from the canonical side. [Based on https://arxiv.org/abs/2604.12854 and https://arxiv.org/abs/2510.26520]