Groups of special matchings and Bruhat graph automorphisms

Abstract

Given any Weyl group W, the groups generated by special matchings on the Bruhat order of W have been introduced, and it turns out that those groups are not necessarily reflection groups. In addition, the SageMath algorithm has been constructed, and from it, it was proven that for any butterfly in types B2 up to B9, D4 up to D6 and E6 there must be an element that coves ( or that is covered) by the maximal (or minimal) elements of that butterfly. This result have been used to prove Proposition 3.2.10 which is the second main result of this dissertation.