  We examine a discrete-time Markovian particle system on the quarter-plane
introduced by M. Defosseux. The vertical boundary acts as a reflecting wall.
The particle system lies in the Anisotropic Kardar-Parisi-Zhang with a wall
universality class. After projecting to a single horizontal level, we take the
longtime asymptotics and obtain the discrete Jacobi and symmetric Pearcey
kernels. This is achieved by showing that the particle system is identical to a
Markov chain arising from representations of the infinite-dimensional
orthogonal group. The fixed-time marginals of this Markov chain are known to be
determinantal point processes, allowing us to take the limit of the correlation
kernel.
  We also give a simple example which shows that in the multi-level case, the
particle system and the Markov chain evolve differently.
