Bruhat Order on Partial Fixed Point Free Involutions

Abstract

The order complex of inclusion poset $P{F}_n$ of Borel orbit closures in skew-symmetric matrices is investigated. It is shown that $P{F}_n$ is an EL-shellable poset, and furthermore, its order complex triangulates a ball. The rank-generating function of $P{F}_n$ is computed and the resulting polynomial is contrasted with the Hasse-Weil zeta function of the variety of skew-symmetric matrices over finite fields.

Minor typos are fixed