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