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The field equations are proposed for the third rank tensor field with thehook Young diagram. The equations describe the irreducible spin two masslessrepresentation in any $d\geq 3$. The starting point of the construction is thelinearised system of Einstein equations which includes the Nordstr\"omequation. This equation, being considered irrespectively to the rest of theEinstein system, corresponds to the topological field theory. The generalsolution is a pure gauge, modulo topological modes which we neglect in thisarticle. We find the sequence of the reducible gauge transformations for thelinearised Nordstr\"om equation, with the hook tensor being the initial gaugesymmetry parameter. By substituting the general solution of the Nordstr\"omequation into the rest of the Einstein's system, we arrive at the fieldequations for the hook tensor. The degree of freedom number count confirms, itis the spin two theory.

Gauge symmetry of linearised Nordstr\"om gravity and the dual spin two field theory