Abstract

We study the irreducible representations of the symmetric group n over a eld F of positive characteristic p. For convenience, but no loss of generality, we shall assume that F is algebraically closed. Let = (1 2 : : : l > 0) be a partition of n. As usual the set of nodes [] := f(i; j) 2 Z2 j 1 i l; 1 j ig is called the Young diagram of . We represent [] as a set of square boxes in Z2, by placing a square with opposite corners (i 􀀀 1; j 􀀀 1) and (i; j), for each (i; j) 2 []. In accordance with the anglo-american convention, we orient the positive direction of the Y -axis downwards. The transpose 0 of is the partition of n dened by 0 i = #fj j j ig, for all i. The Young diagram of 0 is obtained from [] by re ection in the main diagonal.