Fermions are expressible in terms of polynomials in the canonical generators and their ∗-conjugates of the Cuntz algebra . A canonical construction of such fermions is called a recursive fermion system. In this paper, various unital ∗-endomorphisms of the algebra of fermions are explicitly constructed by using the recursive fermion system. We investigate how such endomorphisms transform the Fock representation, the infinite wedge representation, and their duals.
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