Fixed point sets for permutation modules

2009/01/28 by Peter Collings, Collings, Peter
Computer Science · Engineering · Mathematics · #20C20 #Advanced Differential Equations and Dynamical Systems #Coding theory and cryptography #FOS: Mathematics #Representation Theory (math.RT) #graph theory and CDMA systems #math.RT #msc:20C20

paper · pdf · doi:10.48550/arxiv.0901.4378

26 pages

arxiv created 2009/01/28 · openalex publication_date 2009/01/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the representation of the symmetric group afforded by the action on its conjugacy class of fixed point free involutions, over an algebraically closed field of finite characteristic p. We discuss the general form of the set of involutions fixed by an arbitrary vertex of an irreducible component of the module afforded by the action, and show how such a set is composed of certain basic fixed point sets which we can enumerate in the case p = 2. The Broué correspondence allows us to pass from the fixed point sets to the vertices.

Related

• The 2-modular permutation modules on fixed point free involutions of symmetric groups
• Characteristic classes of involutions in nonsolvable groups
• Conjugacy in Permutation Representations of the Symmetric Group
• k-involutions of SL(n,k) over Fields of Characteristic 2
• Projective modules and involutions