  In this paper we discuss the second bosonization of the Hirota bilinear
equation for the CKP hierarchy introduced by Date, Jimbo, Kashiwara and Miwa.
We show that there is a second, untwisted, Heisenberg action on the Fock space,
in addition to the twisted Heisenberg action suggested by Date, Jimbo,
Kashiwara and Miwa and studied by van de Leur, Orlov and Shiota. We derive the
decomposition of the Fock space into irreducible Heisenberg modules under this
action. We show that the space spanned by the highest weight vectors of the
irreducible Heisenberg modules has a structure of a super vertex algebra,
specifically the symplectic fermions vertex algebra. We complete the second
bosonization of the CKP Hirota equation by expressing the generating field via
exponentiated boson vertex operators acting on a polynomial algebra with two
infinite sets of variables.
