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We consider a massless higher spin field theory within the BRST approach andconstruct a general off-shell cubic vertex corresponding to irreducible higherspin fields of helicities $s_1, s_2, s_3$. Unlike the previous works on cubicvertices, which do not take into account of the trace constraints, we use thecomplete BRST operator, including the trace constraints that describe anirreducible representation with definite integer helicity. As a result, wegeneralize the cubic vertex found in [arXiv:1205.3131 [hep-th]] and calculatethe new contributions to the vertex, which contain additional terms with asmaller number space-time derivatives of the fields as well as the termswithout derivatives.

General Cubic Interacting Vertex for Massless Integer Higher Spin Fields