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