Demazure模的简化表现与嵌入
Simplified presentations and embeddings of Demazure modules
AI总结：
该研究针对非扭仿射李代数，通过简化Demazure模的表现，证明了高阶Demazure模到低阶模张量积的嵌入，并提出晶体论方法求解其关于极大半单李子代数的经典分解。
摘要：
针对非扭仿射李代数，我们证明了任意更高阶Demazure模均可嵌入到更低阶Demazure模的张量积中（例如A型情形下的1阶模）；当取反支配权的极限时，该嵌入会退化为熟知的、底层单李代数的有限维不可约模到基本模张量积中的嵌入。为实现这一目标，我们首先简化了这些模的表现，将CV13的结果推广到$\boldsymbol{\frak{g}}$-稳定的情形。作为应用，我们提出了一种晶体论方法，通过将Demazure晶体识别为对应晶体张量积中的连通分支，来求解关于极大半单李子代数的经典分解。
英文摘要：
For an untwisted affine Lie algebra we prove an embedding of any higher level Demazure module into a tensor product of lower level Demazure modules (e.g. level one in type A) which becomes in the limit (for anti-dominant weights) the well-known embedding of finite-dimensional irreducible modules of the underlying simple Lie algebra into the tensor product of fundamental modules. To achieve this goal, we first simplify the presentation of these modules extending the results of \cite{CV13} in the $\mathfrak{g}$-stable case. As an application, we propose a crystal theoretic way to find classical decompositions with respect to a maximal semi-simple Lie subalgebra by identifying the Demazure crystal as a connected component in the corresponding tensor product of crystals.
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