  We show that the symplectic and orthogonal character analogues of Okounkov's
Schur measure (on integer partitions) are determinantal, with explicit
correlation kernels. We apply this to prove certain
Borodin-Okounkov-Gessel-type results concerning Toeplitz+Hankel and Fredholm
determinants; a Szeg\H{o}-type limit theorem; an edge Baik-Deift-Johansson-type
asymptotical result for certain symplectic and orthogonal analogues of the
poissonized Plancherel measure; and a similar result for actual poissonized
Plancherel measures supported on "almost symmetric" partitions.
