Finding PPT states with high Schmidt numbers has recently emerged as a significant mathematical challenge in quantum information theory. In this talk, we present a broad family of such examples by considering bipartite states invariant under symplectic group actions. By applying a general group symmetry method, we derive a two-parameter family of PPT states on $\mathbb{C}^d\otimes \mathbb{C}^d$ that have Schmidt number exactly $d/2$ which is the best-known bounds in literature. On the dual side, we also provide a two-parameter characterization of ($d/2-1$)-positive linear maps between $M_d(\mathbb{C})$ that are indecomposable.