任意权下量子Lakshmibai-Seshadri路径的推广
A generalization of quantum Lakshmibai-Seshadri paths for arbitrary weights
AI总结：
该研究构造了量子凹室模型可允许子集到插值QLS路径的保权单射，推广了量子Lakshmibai-Seshadri路径，并以此重述了量子仿射代数零级极值权模Demazure子模分次特征的Chevalley型恒等式。
摘要：
我们构造了一个单射的保权映射（称为遗忘映射），其定义域是与任意权相关的量子凹室模型中所有可允许子集的集合。通过引入“插值量子Lakshmibai-Seshadri（简称QLS）路径”的概念，可以明确描述该遗忘映射的像，这类路径可视为量子Lakshmibai-Seshadri路径的推广。作为应用，我们利用插值QLS路径重新表述了量子仿射代数上零级极值权模的Demazure子模的分次特征的Chevalley型恒等式，该恒等式是半无限旗流形的环面等变$K$-群的Chevalley公式在表示论中的对应物。
英文摘要：
We construct an injective weight-preserving map (called the forgetful map) from the set of all admissible subsets in the quantum alcove model associated to an arbitrary weight. The image of this forgetful map can be explicitly described by introducing the notion of "interpolated quantum Lakshmibai-Seshadri (QLS for short) paths", which can be thought of as a generalization of quantum Lakshmibai-Seshadri paths. As an application, we reformulate, in terms of interpolated QLS paths, an identity of Chevalley type for the graded characters of Demazure submodules of a level-zero extremal weight module over a quantum affine algebra, which is a representation-theoretic analog of the Chevalley formula for the torus-equivariant $K$-group of a semi-infinite flag manifold.
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