  Representation of the algebra of FP (anti)ghosts in string theory is studied
by generalizing the recursive fermion system in the Cuntz algebra constructed
previously. For that purpose, the pseudo Cuntz algebra, which is a
$\ast$-algebra generalizing the Cuntz algebra and acting on indefinite-metric
vector spaces, is introduced. The algebra of FP (anti)ghosts in string theory
is embedded into the pseudo Cuntz algebra recursively in two different ways.
Restricting a certain permutation representation of the pseudo Cuntz algebra,
representations of these two recursive FP ghost systems are obtained. With
respect to the zero-mode operators of FP (anti)ghosts, it is shown that one
corresponds to the four-dimensional representation found recently by one of the
present authors (M.A.) and Nakanishi, while the other corresponds to the
two-dimensional one by Kato and Ogawa.
