Partially-massless higher spin algebras in four dimensions

We propose a realisation of partially-massless higher spin algebras in four dimensions in terms of bosonic and fermionic oscillators, using Howe duality between sp(4, ℝ) ≅ so(2, 3) and osp(1|2(ℓ − 1), ℝ). More precisely, we show that the centraliser of osp(1|2(ℓ − 1), ℝ) in the Weyl-Clifford algebra generated by 4 bosonic and 8(ℓ − 1) fermionic symbols, modulo osp(1|2(ℓ − 1), ℝ) generators, is isomorphic to the higher spin algebra of the type-A_ℓ theory whose spectrum contains partially-massless fields of all spins and depths t = 1, 3,…, 2ℓ − 1. We also discuss the possible existence of a deformation of this algebra, which would encode interaction for the type-A_ℓ theory.