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THE INFINITE-DIMENSIONAL p-ADIC SYMPLECTIC GROUP

An analogue of the Fock representation is constructed for the infinite-dimensional p-adic Heisenberg group.The restricted symplectic group is defined for an infinite-dimensional symplectic space over the field Qp of p-adic numbers. For the restricted symplectic group a projective representation is constructed that is compatible with the representation of the Heisenberg group, and an expression for the cocycle of this representation is given in terms of the p-adic Maslov index. It is proved that the extension corresponding to this cocycle reduces to a Z2-extension.