Dual Kashiwara Functions for the B(∞) Crystal
Dual Kashiwara Functions for the B(∞) Crystal
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B(∞) 晶体的对偶 Kashiwara 函数
DOI：
10.1007/978-3-030-02191-7_8
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
A. Joseph
中科院分区：
文献类型：
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作者：
A. Joseph
设g是Kac-Moody代数。对于每个约化Weyl群元素的序列J，Kashiwara构造了一个crystalBJ，它作为一个集合与秩的自由N模相同|J|并证明了它含有一个“最高权”的亚晶BJ（∞），具有一些显著的组合性质。本文的目的是通过对每个单根α构造一组对偶Kashiwara函数来将BJ（∞）表示为BJ的一个显式多面体子集，这些对偶Kashiwara函数是BJ上的一个线性函数，其最大值限制在BJ（∞）上，从而确定对偶Kashiwara参数。根据有关Demazure模中的恒等式的自然猜想，证明了这些函数是通过相对于g的朗兰兹对偶的最低权重ta的基本模Jin相当明确地确定的“踪迹”给出的。证明使用Kashiwara对偶扩展到非对称化的情况下，作者开发的S-图的理论。
Let g be a Kac-Moody algebra. For each sequenceJof reduced Weyl group elements, Kashiwara constructed a crystalBJwhich as a set identifies with the free N module of rank |J| and showed that it contains a “highest weight” subcrystalBJ(∞) having some remarkable combinatorial properties. The goal of the present work is to exhibitBJ(∞) as an explicit polyhedral subset ofBJby constructing for each simple root α, a set of dual Kashiwara functions which are linear functions onBJand whose maximum restricted toBJ(∞) determines the dual Kashiwara parameter. Up to a natural conjecture concerning identities in the Demazure modules, it is shown that these functions are given through rather explicitly determined “trails” with respect toJin the fundamental module of lowest weighta for the Langlands dual of g. The proof uses Kashiwara duality extended to the non-symmetrizable case and the theory of S-graphs developed by the author.