Linearized Coxeter Higher-Spin Theories

A class of higher-spin gauge theories on $AdS_4$ associated with various Coxeter groups $\mathcal{C}$ is analyzed at the linear order. For a general $\mathcal{C}$, a solution corresponding to the $AdS_4$ space and the form of the free unfolded equations are established. A disentanglement criterion has been formulated for Coxeter HS modules. The shifted homotopy technique is uplifted to the general Coxeter HS models. In case of the Coxeter group $B_2$ classification of unitary HS modules and a consistent truncation to them are determined, the dynamical content is discussed briefly.