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 { x 1 , …, x n ], where x 1 ,…, x n are independent indeterminates over K . The group algebra of S n with coefficients in K is denoted by Ф n .