Admissible Sequences for Twisted Involutions in Weyl Groups

Abstract

AbstractLetW be a Weyl group, Σ a set of simple reflections inW related to a basis Δ for the root system Φ associated with W and θ an involution such that θ(Δ) = Δ. We show that the set of θ- twisted involutions in W, = {w ∈ W | θ(w) = w–1} is in one to one correspondence with the set of regular involutions . The elements of are characterized by sequences in Σ which induce an ordering called the Richardson–Springer Poset. In particular, for Φ irreducible, the ascending Richardson–Springer Poset of , for nontrivial θ is identical to the descending Richardson–Springer Poset of .