Tensor product decomposition theorem for quantum Lakshmibai-Seshadri paths and standard monomial theory for semi-infinite Lakshmibai-Seshadri paths
Tensor product decomposition theorem for quantum Lakshmibai-Seshadri paths and standard monomial theory for semi-infinite Lakshmibai-Seshadri paths
复制标题
量子 Lakshmibai-Seshadri 路径的张量积分解定理和半无限 Lakshmibai-Seshadri 路径的标准单项式理论
DOI：
10.1016/j.jcta.2019.105122
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
and D. Sagaki
中科院分区：
文献类型：
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作者：
S. Naito;F. Nomoto;and D. Sagaki
设λ是无扭仿射李代数的（零级）支配整权，QLS（λ）表示形状为λ的量子Lakshmibai-Seshadri（QLS）路集.对于有限Weyl群W的元素w，非对称Macdonald多项式Ew λ（q，t）在t= 0和t=∞处的特化用形状为λ的QLS路和定义在其上的度函数来明确描述.此外，对于（零级）主导积分权重λ，μ，我们有晶体的同构Θ：QLS（λ+ μ）→ QLS（λ）<$QLS（μ）。本文通过半无限Lakshmibai-Seshadri（LS）路与QLS路的关系，研究了度函数在晶体同构Θ下的行为.作为应用，我们给出了广义Weyl模分次特征标的一个递归公式的晶体理论证明.
Let λ be a (level-zero) dominant integral weight for an untwisted affine Lie algebra, and let QLS (λ) denote the set of quantum Lakshmibai-Seshadri (QLS) paths of shape λ. For an element w of a finite Weyl group W, the specializations at t= 0 and t=∞ of the nonsymmetric Macdonald polynomial E w λ (q, t) are explicitly described in terms of QLS paths of shape λ and the degree function defined on them. Also, for (level-zero) dominant integral weights λ, μ, we have an isomorphism Θ: QLS (λ+ μ)→ QLS (λ)⊗ QLS (μ) of crystals. In this paper, we study the behavior of the degree function under the isomorphism Θ of crystals through the relationship between semi-infinite Lakshmibai-Seshadri (LS) paths and QLS paths. As an application, we give a crystal-theoretic proof of a recursion formula for the graded characters of generalized Weyl modules.