Quiver Varieties and Path Realizations arising from Adjoint Crystals of type $A_n^{(1)}$

Details Quiver Varieties and Path Realizations arising from Adjoint Crystals of type $A_n^{(1)}$ Quiver Varieties and Path Realizations arising from Adjoint Crystals of type $A_n^{(1)}$

2010-09-13

arxiv.org/abs/1009.2355v2

Mathematics

Representation Theory

This is accepted for publication by Transactions of the American Mathematical Society

Scientific paper

Let $B(\Lambda_0)$ be the level 1 highest weight crystal of the quantum
affine algebra $U_q(A_n^{(1)})$. We construct an explicit crystal isomorphism
between the geometric realization $\mathbb{B}(\Lambda_0)$ of $B(\Lambda_0)$ via
quiver varieties and the path realization ${\mathcal P}^{\rm ad}(\Lambda_0)$ of
$B(\Lambda_0)$ arising from the adjoint crystal $\adjoint$.

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