Iterating Lowering Operators
نویسنده
چکیده
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 Si,j(A)fμ,λ is a non-zero GL(n − 1)-high weight vector, where Si,j(A) is Kleshchev’s lowering operator and fμ,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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