BMW Algebra, quantized coordinate algebra and type C schur–weyl duality

We prove an integral version of the Schur–Weyl duality between the specialized Birman–Murakami–Wenzl algebra B_n(−q^2m+1, q) and the quantum algebra associated to the symplectic Lie algebra (formula presented)_2m. In particular, we deduce that this Schur–Weyl duality holds over arbitrary (commutative) ground rings, which answers a question of Lehrer and Zhang in the symplectic case. As a byproduct, we show that, as a ℤ[q, q⁻¹]-algebra, the quantized coordinate algebra defined by Kashiwara (which he denoted by A^ℤ_q (g)) is isomorphic to the quantized coordinate algebra arising from a generalized Faddeev–Reshetikhin–Takhtajan construction.