Properties of Twisted Involutions in Signed Permutation Notation

In algebraic contexts, Weyl group elements are usually represented in terms of generators and relations, where representation is not unique. For computational purposes, a more combinatorial representation for elements of classical Weyl groups as signed permutation vectors was introduced in [5]. This paper characterizes some special classes of Weyl group elements using this notation. These classes are especially useful for the study of symmetric spaces and their representations.