Sects and lattice paths over the Lagrangian Grassmannian (Q2309221)

Summary: We examine Borel subgroup orbits in the classical symmetric space of type \(CI\), which are parametrized by skew symmetric \((n,n)\)-clans. We describe bijections between such clans, certain weighted lattice paths, and pattern-avoiding signed involutions, and we give a cell decomposition of the symmetric space in terms of collections of clans called sects. The largest sect with a conjectural closure order is isomorphic (as a poset) to the Bruhat order on partial involutions.