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.
An introduction to the representation theory of Temperley–Lieb algebras.Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam, 2015
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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.