  We pursue applications for symplectic Plancherel growth based on a repulsion
phenomenon arising in its diffusion limit and on intermediate representation
theory underlying its correlation structure. Under diffusive scaling, the
dynamics converge to interlaced reflecting Brownian motions with a wall that
achieve Dyson non-colliding dynamics. We exhibit non-degeneracy of constraint
in this coupled system by deriving a path property that quantifies repulsion
between particles coinciding in the limit. We then identify consistent series
of Plancherel measures for $Sp(\infty)$ that reflect the odd symplectic groups,
despite their non-semisimplicity. As an application, we compute the correlation
kernel of the growth model and investigate its local asymptotics: the
incomplete beta kernel emerges in the bulk limit, and new variants of the
Jacobi and Pearcey kernels arise as edge limits. In particular, we provide
further evidence for the universality of the $1/4$-growth exponent and Pearcey
point process in the class of anisotropic KPZ with a wall.
