On Demazure crystals for 𝑈_{𝑞}(𝐺₂⁽¹⁾)

Jayne, Rebecca; Misra, Kailash

doi:10.1090/S0002-9939-2010-10663-9

On Demazure crystals for $U_q(G_2^{(1)})$
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by Rebecca L. Jayne and Kailash C. Misra PDF

Proc. Amer. Math. Soc. 139 (2011), 2343-2356 Request permission

Abstract:

We show that there exist suitable sequences $\{w^{(k)}\}_{k \ge 0}$ and $\{w’^{(k)}\}_{k \ge 0}$ of Weyl group elements for a given perfect crystal of level $l\ge 1$ such that the path realizations of the Demazure crystals $B_{w^{(k)}}(l\Lambda _0)$ and $B_{w’^{(k)}}(l\Lambda _2)$ for the quantum affine algebra $U_q(G_2^{(1)})$ have tensor-product-like structures with mixing index $\kappa =1$.

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