Conformal wave expansions for flat space amplitudes

The extended BMS algebra contains a conformal subgroup that acts on the celestial sphere as SO(1, 3). It is of interest to perform mode expansions of free fields in Minkowski spacetime that realize this symmetry in a simple way. In the present work we perform such a mode expansion for massive scalar fields using the unitary principal series representations of SO(1, 3) with a view to developing a holographic approach to gravity in asymptotically flat spacetime. These mode expansions are also of use in studying holography in three-dimensional de Sitter spacetime.

Branching laws for small unitary representations of GL(n, ℂ)

The unitary principal series representations of G = GL (n, ℂ) induced from a character of the maximal parabolic subgroup P = ( GL (1, ℂ) × GL (n - 1, ℂ)) ⋉ ℂn-1 attain the minimal Gelfand–Kirillov dimension among all infinite-dimensional unitary representations of G. We find the explicit branching laws for the restriction of these representations to all reductive subgroups H of G such that (G, H) forms a symmetric pair.