Counting Borel Orbits in Symmetric Spaces of Types BI and CII

Abstract

This is a continuation of our combinatorial program on the enumeration of Borel orbits in symmetric spaces of classical types. Here, we determine the generating series the numbers of Borel orbits in $${\mathbf {SO}}_{2n+1}/{\mathbf {S(O}}_{2p}\times {\mathbf {O}}_{2q+1} \mathbf {)}$$ (type BI) and in $${\mathbf {Sp}}_n/{\mathbf {Sp}}_p \times {\mathbf {Sp}}_q$$ (type CII). In addition, we explore relations to lattice path enumeration.