Sects and Lattice Paths over the Lagrangian Grassmannian

• DOI: 10.37236/8664
• Publication Date: 2020-03-19T00:37:33Z
• Authors: Aram Bingham; Özlem Uğurlu
• Keywords: 05A15, 14M15, 14M17; FOS: Mathematics; Mathematics - Combinatorics; Combinatorics (math.CO); 0101 mathematics; 01 natural sciences

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.