Quiver varieties and adjoint crystals of level $\ell$ for type $A_n^{(1)}$

Abstract

Let $B(\Lambda )$ be a level $\ell$ highest weight crystal of the quantum affine algebra $U_q(A_n^{(1)})$. We construct an explicit crystal isomorphism between the geometric realization $\gB(Λ)$ of the crystal $B(\Lambda )$ using quiver varieties and the path realization ${\mathcal{P}}^{\mathrm{ad}}(\Lambda )$ arising from the adjoint crystal $\Bad{\ell}$ of level $\ell$.

Typos are corrected

References in corpus (3)

• Level 1 Perfect Crystals and Path Realizations of Basic Representations at q=0
• Geometric and combinatorial realizations of crystal graphs
• Quiver Varieties and Path Realizations arising from Adjoint Crystals of type $A_n^{(1)}$