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We study the massless irreducible representations of the Poincar\'{e} groupin the six-dimensional Minkowski space. The Casimir operators are constructedand their eigenvalues are found. It is shown that the finite spin (helicity)representation is defined by two integer or half-integer numbers while theinfinite spin representation is defined by the real parameter $\mu^2$ and oneinteger or half-integer number.

Massless finite and infinite spin representations of Poincar\'{e} group in six dimensions