Computing Admissible Sequences for Twisted Involutions in Weyl Groups
نویسنده
چکیده
Let (W,6) be a finite Coxeter system, and θ an involution such that θ(1) = 1, where 1 is a basis for the root system 8 associated with W . We show that the set of θ-twisted involutions in W , Iθ = {w ∈ W | θ(w) = w−1} is in one to one correspondence with the set of regular involutions IId. The elements of Iθ are characterized by sequences in 6 which induce an ordering called the Bruhat Lattice. In particular, for 8 irreducible, the ascending Bruhat Lattice of Iθ, for nontrivial θ is identical to the descending Bruhat Lattice of IId.
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