Iterating lowering operators

For an algebraically closed base field of positive characteristic, an algorithm to construct some non-zero GL(n-1)GL(n-1)-high weight vectors of irreducible rational GL(n)GL(n)-modules is suggested. It is based on the criterion proved in this paper for the existence of a set A   such that Si,n(A)fμ,λSi,n(A)fμ,λ is a non-zero GL(n-1)GL(n-1)-high weight vector, where Si,n(A)Si,n(A) is Kleshchev's lowering operator and fμ,λfμ,λ is a non-zero GL(n-1)GL(n-1)-high weight vector of weight μμ of the costandard GL(n)GL(n)-module ∇n(λ)∇n(λ) with highest weight λλ.