Quiver Varieties and Adjoint Crystals of Level ℓ for TypeA_n⁽¹⁾

Abstract

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