Extended symmetric spaces and θ-twisted involution graphs. Issue 6 (2nd June 2020)

• Record Type: Journal Article
• Authors: Collins, J. B.; Haas, Ruth; Helminck, Aloysius G.; Lenarz, Jessie; Pelatt, Kristine Engel; Saccon, Silvia; Welz, Matthew
• Is Part Of: Communications in algebra. Volume 48:Issue 6(2020)
• Page Start: 2293
• Page End: 2306
• Publication Date: 2020-06-02
• Subjects: Algebraic combinatorics -- symmetric spaces; 05E15 -- 05E25 -- 20F55 -- 05C25; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1711106
• Languages: English
• ISSNs: 0092-7872

Abstract

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 .