Abstract
Let B(Λ) be a level ℓ highest weight crystal of the quantum affine algebra . We construct an explicit crystal isomorphism between the geometric realization 𝔅(Λ) of the crystal B(Λ) using quiver varieties and the path realization 𝒫ad(Λ) arising from the adjoint crystal B ad, ℓ of level ℓ.
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