Closures of K-orbits in the flag variety for GL(2n)

TL;DR

This paper characterizes the rationally smooth closures of K-orbits in the flag variety for GL(2n) using graph-theoretic criteria and proposes a pattern avoidance criterion for rational smoothness.

Contribution

It introduces a graph-theoretic characterization of rationally smooth orbit closures and proposes a conjecture on pattern avoidance for sufficiency.

Findings

Graph-theoretic criterion for rational smoothness

Necessary pattern avoidance criterion for rational smoothness

Conjecture on sufficiency of pattern avoidance

Abstract

We characterize the O_{2n} orbits in the flag variety for GL_{2n} with rationally smooth closure via a graph-theoretic criterion. We also give a necessary pattern avoidance criterion for rational smoothness and conjecture its sufficiency.