A simpler diagrammatic construction via the Temperley-Lieb algebra yields explicit formulas for the entire dual canonical basis in (C^2)^⊗n and reproves its duality with the canonical basis.
Quivers, perverse sheaves, and quantized enveloping algebras.Journal of the American Mathe- matical Society, 4(2):365–421, 1991
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The Dual Canonical Basis in the Spin Representation via the Temperley-Lieb Algebra
A simpler diagrammatic construction via the Temperley-Lieb algebra yields explicit formulas for the entire dual canonical basis in (C^2)^⊗n and reproves its duality with the canonical basis.