Commuting Involution Graphs in Classical Affine Weyl Groups

2018/09/13 by Hart, Sarah, Clarke, Amal Sbeiti
#20F55 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1809.04832

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.

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