  We consider the supermultiplet of linearized beta-deformation of
$\mathcal{N}=4$ Super Yang-Mills(SYM). It was previously studied on the
gravitational side. We study the supermultiplet of beta-deformations on the
field theory side and we compare two finite-dimensional representations of
$psl(4|4,\bf{R})$ algebra. We show that they are related by an intertwining
operator. We develop a twistor-based approach which could be useful for
studying other finite-dimensional and nonunitary representations in AdS/CFT
correspondence.
