Abstract
Let K be an algebraically closed field of prime characteristic p. Consider a simple rational module L for the general linear group GL(n,K). Let i be an integer from 1 to n and d be an integer from 1 to p-1. We find the answer in combinatorial terms to the following question: does there exist in L a (nonzero) GL(n-1,K)-primitive vector of weight that is obtained from the highest weight of L by subtracting d from its ith component?