The $\sigma_-$ Cohomology Analysis for Coxeter HS $B_2$ model

The dynamical content of equations resulting from rank-two covariant derivatives in $B_2$ Coxeter theory in $AdS_4$ are analyzed in terms of $\sigma_-$-complexes. Primary fields and gauge-invariant differential operators on primary fields are classified for $(adj \otimes adj)$ one-form fields $\omega$ and $(tw\otimes adj)$ zero-form fields $C$. It is shown that one-forms $\omega$ in the $(adj \otimes adj)$ sector encode symmetric massless fields and partially massless fields of all spins and depth of masslessness. Gluing of the one-form module to the zero-form modules at the linear vertices is studied.