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

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

2010-11-26

arxiv.org/abs/1011.5759v2

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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