Quiver varieties and path realizations arising from adjoint crystals of type 𝐴_{𝑛}⁽¹⁾

Kang, Seok-Jin; Park, Euiyong

doi:10.1090/S0002-9947-2011-05246-3

Quiver varieties and path realizations arising from adjoint crystals of type $A_n^{(1)}$
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by Seok-Jin Kang and Euiyong Park

Trans. Amer. Math. Soc. 363 (2011), 5341-5366

DOI: https://doi.org/10.1090/S0002-9947-2011-05246-3

Published electronically: May 9, 2011

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Abstract:

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 ${\mathcal P}^{\textrm {ad}}(\Lambda _0)$ of $B(\Lambda _0)$ arising from the adjoint crystal $B^{\textrm {ad}}$.

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