  To provide tools, especially L-operators, for use in studies of rational
Yang-Baxter algebras and quantum integrable models when the Lie algebras so(N)
(b_n, d_n) or sp(2n) (c_n) are the invariance algebras of their R matrices,
this paper develops a presentation of these Lie algebras convenient for the
context, and derives many properties of the matrices of their defining
representations and of the ad-invariant tensors that enter their multiplication
laws. Metaplectic-type representations of sp(2n) and so(N) on bosonic and on
fermionic Fock spaces respectively are constructed. Concise general expressions
(see (5.2) and (5.5) below) for their L-operators are obtained, and used to
derive simple formulas for the T operators of the rational RTT algebra of the
associated integral systems, thereby enabling their efficient treatment by
means of the algebraic Bethe ansatz.
