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.
@article{10_37236_8664,
author = {Aram Bingham and \"Ozlem U\u{g}urlu},
title = {Sects and lattice paths over the {Lagrangian} {Grassmannian}},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {1},
doi = {10.37236/8664},
zbl = {1442.14155},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8664/}
}
TY - JOUR
AU - Aram Bingham
AU - Özlem Uğurlu
TI - Sects and lattice paths over the Lagrangian Grassmannian
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/8664/
DO - 10.37236/8664
ID - 10_37236_8664
ER -
%0 Journal Article
%A Aram Bingham
%A Özlem Uğurlu
%T Sects and lattice paths over the Lagrangian Grassmannian
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/8664/
%R 10.37236/8664
%F 10_37236_8664
Aram Bingham; Özlem Uğurlu. Sects and lattice paths over the Lagrangian Grassmannian. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8664
