Mathematics – Representation Theory
Scientific paper
2010-11-26
Mathematics
Representation Theory
24 pages
Scientific paper
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 $\gB(\Lambda)$ of the crystal $B(\Lambda)$
using quiver varieties and the path realization $\mathcal{P}^{\rm ad}(\Lambda)$
arising from the adjoint crystal $\Bad{\ell}$ of level $\ell$.
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