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Article
Extended Symmetric Spaces and θ-twisted Involution Graphs
Mathematics, Data Science, and Statistics Faculty Research
  • Jessie Lenarz, Saint Catherine University
  • Kristine Pelatt, St. Catherine University
  • J B Collins, University of Mary Washington
  • Ruth Haas, University of Hawaii, Manoa
  • Aloysius G Helmink, University of Hawaii, Manoa
  • Silvia Saccon, Bard College
  • Matthew Welz, Fort Lewis College
Document Type
Article
Publication/Presentation Date
2-3-2020
Journal Title
Communications in Algebra
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.

Citation Information
J. B. Collins, Ruth Haas, Aloysius G. Helminck, Jessie Lenarz, Kristine Engel Pelatt, Silvia Saccon & Matthew Welz (2020) Extended symmetric spaces and θ-twisted involution graphs, Communications in Algebra, DOI: 10.1080/00927872.2019.1711106