On the involution module of GLn(2f)GLn(2f)

For any group G   the set of involutions II in G, that is, the set of group elements that have order two, forms a G-set under conjugation. The corresponding kG  -permutation module kIkI is the involution module of G. Here k   is an algebraically closed field of characteristic two. In this paper we discuss aspects of the involution module of the general linear group GLn(2f)GLn(2f). We determine almost all components of this module. Furthermore we present a vertex and the Green correspondent of each component.