Sects and Lattice Paths over the Lagrangian Grassmannian

  • Aram Bingham
  • Özlem Uğurlu

Abstract

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.

Published
2020-03-06
Article Number
P1.51