Equicontinuity Regions and Kulkarni Limit Sets for Discrete Subgroups of Quaternionic Hyperbolic Isometry Groups Acting on Grassmannians

Let Γ be a discrete subgroup of PSp(n,1). We realize Hⁿ⁺¹ as C²ⁿ⁺² and study the induced action of Γ on P (C²ᵏ⁺² C²ⁿ⁺²) where 0≤ k≤ n-1, into which the quaternionic Grassmannian Grₖ₊₁( Hⁿ⁺¹) embeds equivariantly. We determine all pseudo-projective limits of the action. Their images are the linear spans of the $(k+1)$-planes tangent to the boundary at points of the Chen--Greenberg limit set, and their kernels are the orthogonal complements of such spans. As a consequence, we describe the equicontinuity region explicitly, identify the k-Chen-Greenberg limit set with the set of tangent $(k+1)$-planes at limit points, and show that the equicontinuity region is contained in the Kulkarni domain of discontinuity. For non-elementary groups, we also give a lower bound for the Kulkarni limit set in terms of the k-Chen-Greenberg limit set.