  We present a new case of duality between integrable many-body systems, where
two systems live on the action-angle phase spaces of each other in such a way
that the action variables of each system serve as the particle positions of the
other one. Our investigation utilizes an idea that was exploited previously to
provide group-theoretic interpretation for several dualities discovered
originally by Ruijsenaars. In the group-theoretic framework one applies
Hamiltonian reduction to two Abelian Poisson algebras of invariants on a higher
dimensional phase space and identifies their reductions as action and position
variables of two integrable systems living on two different models of the
single reduced phase space. Taking the cotangent bundle of U(2n) as the
upstairs space, we demonstrate how this mechanism leads to a new dual pair
involving the BC(n) trigonometric Sutherland system. Thereby we generalize
earlier results pertaining to the A(n) trigonometric Sutherland system as well
as a recent work by Pusztai on the hyperbolic BC(n) Sutherland system.
