  We introduce a two parameter ($\alpha, \beta>-1$) family of interacting
particle systems with determinantal correlation kernels expressible in terms of
Jacobi polynomials $\{ P^{(\alpha, \beta)}_k \}_{k \geq 0}$. The family
includes previously discovered Plancherel measures for the infinite-dimensional
orthogonal and symplectic groups. The construction uses certain BC-type
orthogonal polynomials which generalize the characters of these groups.
  The local asymptotics near the hard edge where one expects distinguishing
behavior yields the multi-time $(\alpha, \beta)$-dependent discrete Jacobi
kernel and the multi-time $\beta$-dependent hard-edge Pearcey kernel. For
nonnegative integer values of $\beta$, the hard-edge Pearcey kernel had
previously appeared in the asymptotics of non-intersecting squared Bessel paths
at the hard edge.
