Embeddings Among Quantum Affine sl_n
Embeddings Among Quantum Affine sl_n
复制标题
量子仿射 sl_n 中的嵌入
DOI：
10.1007/s10114-023-2073-2
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Li, Yi Qiang
中科院分区：
文献类型：
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作者：
Li, Yi Qiang
我们建立了量子仿射到量子仿射的显式嵌入。这种嵌入作为两种自然的，但看似无关的嵌入的共同推广，一个在量子仿射舒尔代数水平上，另一个在非量子水平上。量子仿射舒尔代数上的嵌入被广泛应用于量子仿射正则基的分析。Riche和Williamson在研究有限域上一般线性群的模表示理论时，在非量子水平上的嵌入被重要地使用。在Maksimau关于仿射一般线性代数的范畴表示的工作中也使用了相同的嵌入。我们进一步提供了幂等版本上的嵌入与量子仿射舒尔代数水平上的嵌入的更自然的兼容性陈述。建立了该嵌入的a -变体。
We establish an explicit embedding of a quantum affineinto a quantum affine. This embedding serves as a common generalization of two natural, but seemingly unrelated, embeddings, one on the quantum affine Schur algebra level and the other on the non-quantum level. The embedding on the quantum affine Schur algebras is used extensively in the analysis of canonical bases of quantum affineand. The embedding on the non-quantum level is used crucially in a work of Riche and Williamson on the study of modular representation theory of general linear groups over a finite field. The same embedding is also used in a work of Maksimau on the categorical representations of affine general linear algebras. We further provide a more natural compatibility statement of the embedding on the idempotent version with that on the quantum affine Schur algebra level. A-variant of the embedding is also established.