Commuting involution graphs in classical affine Weyl groups. Issue 7 (2nd July 2020)

• Record Type: Journal Article
• Authors: Hart, Sarah; Sbeiti Clarke, Amal
• Is Part Of: Communications in algebra. Volume 48:Issue 7(2020)
• Page Start: 2941
• Page End: 2957
• Publication Date: 2020-07-02
• Subjects: Affine Weyl group -- commuting involution graph; 20F55 -- 05E18; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1726365
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: In this paper we investigate commuting involution graphs in classical affine Weyl groups. Let W be a classical Weyl group of rank n, with W ˜ its corresponding affine Weyl group. Our main result is that if X is a conjugacy class of involutions in W ˜, then the commuting involution graph C ( W ˜, X ) is either disconnected or has diameter at most n + 2. This bound is known to hold for types A ˜ n and C ˜ n, so the main work of this paper is to prove the theorem for types B ˜ n and D ˜ n .