Counting Borel Orbits in Symmetric Varieties of Types $BI$ and $CII$

Abstract

This is a continuation of our combinatorial program on the enumeration of Borel orbits in symmetric varieties of classical types. Here, we determine the generating series the numbers of Borel orbits in ${\mathbf{SO}}_{2n+1}/{\mathbf{S}(\mathbf{O}}_{2p}\times {\mathbf{O}}_{2q+1})$ (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.

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References in corpus (2)

• Governing singularities of symmetric orbit closures
• The genesis of involutions (polarizations and lattice paths)

Cited by in corpus (1)

• Atoms for signed permutations