Several remarks on the representation of the infinite-dimensional symplectic group and on the construction of the metaplectic group (Q1889672)

Bogolyubov transformations are used to construct a projective representation of the symplectic group of an infinite dimensional symplectic space together with the Mackey extension of some subgroups of the symplectic group. An operator-valued function (defined on a subgroup of the symplectic group) which can be extended to a unitary representation of the Mackey extension constructed from the cocycle corresponding to this operator-valued function is used in the construction of the Mackey extension. A class of the subgroups of the symplectic group (which includes the symplectic group itself in the finite dimensional case) is described for which there is a two-sheeted covering thus implying a construction of the metaplectic group.