Hook representations of the symmetric groups

Abstract

In this paper we are concerned with the representation theory of the symmetric groupsover a field K of characteristic p. Every field is a splitting field for the symmetric groups. Consequently, in order to study the modular representation theory of these groups, it is sufficient to work over the prime fields. However, we take K to be an arbitrary field of characteristic p, since the presentation of the results is not affected by this choice. S_n denotes the group of permutations of {x₁, …, x_n], where x₁,…,x_n are independent indeterminates over K. The group algebra of S_n with coefficients in K is denoted by Ф_n.