Suborbits of a point-stabilizer in the unitary group on the last subconstituent of Hermitean dual polar graphs

Let Γ be a dual polar graph in a unitary space. It is well-known that a point-stabilizer in the unitary group is transitive on the last subconstituent Λ of Γ. In this paper, we determine all the suborbits of this action, calculate its rank and the length of each suborbit. Note that the induced subgraph on Λ is quasi-strongly regular. As an application of our results, all its parameters are computed.