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The local free action principle for bosonic unconstrained higher spin gauge fields in $d$-dimensional (A)dS$_d$ space has been already established by Segal. In this paper, we will present a similar action principle \`a la Segal for fermions. Moreover, we will demonstrate how the Fronsdal and the Fang-Fronsdal equations in $d$-dimensional (A)dS$_d$ space are related, respectively, to the Euler-Lagrange equations of the bosonic and fermionic actions mentioned above.
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