Algorithms for Twisted Involutions in Weyl Groups

Abstract

Let (W, Σ) be a finite Coxeter system, and θ an involution such that θ (Δ) = Δ, where Δ is a basis for the root system Φ associated with W, and [Formula: see text] the set of θ-twisted involutions in W. The elements of [Formula: see text] can be characterized by sequences in Σ which induce an ordering called the Richardson-Spinger Bruhat poset. The main algorithm of this paper computes this poset. Algorithms for finding conjugacy classes, the closure of an element and special cases are also given. A basic analysis of the complexity of the main algorithm and its variations is discussed, as well experience with implementation.