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arxiv: 1210.6464 · v1 · pith:HNBHOEJYnew · submitted 2012-10-24 · 🧮 math.RT · math.QA

R\'eflexions dans un cristal

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keywords lambdacrystalweightelementinftyotimesparametersalgebra
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Let g = n^- + h + n^+ be a symmetrizable Kac-Moody algebra. Let B(\infty) be the Kashiwara crystal of U_q(n^-), let \lambda be a dominant integral weight, let T_\lambda = {t_\lambda} be the crystal with one element of weight \lambda, and let B(\lambda) \subset B(\infty) \otimes T_\lambda be the crystal of the integrable representation of highest weight \lambda. We compute the descending string parameters of an element b \otimes t_\lambda in B(\lambda) in terms of the Lusztig parameters of b.

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