Abstract
We prove that the quantized Carter–Lusztig basis for a finite-dimensional irreducible Uq(𝔤𝔩n(ℂ))-module V(λ) is related to the global crystal basis for V(λ) by an upper triangular invertible matrix. We express the global crystal basis in terms of the q-Schur algebra and provide an algorithm for obtaining global crystal basis vectors for V(λ) using the q-Schur algebra.
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