Extended symmetric spaces and θ-twisted involution graphs. Issue 6 (2nd June 2020) - Collins, J. B.; Haas, Ruth; Helminck, Aloysius G.; Lenarz, Jessie; Pelatt, Kristine Engel; Saccon, Silvia; Welz, Matthew
Abstract: For a Weyl group G and an automorphism θ of order 2, the set of involutions and θ -twisted involutions can be generated by considering actions by basis elements, creating a poset structure on the elements. Haas and Helminck showed that there is a relationship between these sets and their Bruhat posets. We extend that result by considering other bases and automorphisms. We show for G = Sn, θ an involution, and any basis consisting of transpositions, the extended symmetric space is generated by a similar algorithm. Moreover, there is an isomorphism of the poset graphs for certain bases and θ .