论文标题
嵌入量子仿射$ \ mathfrak {sl} _n $
Embeddings among quantum affine $\mathfrak{sl}_n$
论文作者
论文摘要
我们将量子仿射$ \ mathfrak {sl} _n $的显式嵌入到量子仿射$ \ mathfrak {sl} _ {n+1} $中。这种嵌入是两个天然但看似无关的嵌入的常见概括，一个是量子仿射schur代数水平，另一个在非量词水平上。量子Aggine Schur代数上的嵌入在对量子仿射$ \ Mathfrak {Sl} _n $和$ \ Mathfrak {gl} _n $的规范基础的分析中。在有限领域，在Riche and Williamson的研究中，在Riche和Williamson的研究研究中，将嵌入在非量化水平上的嵌入至关重要。 Maksimau的作品中也使用了相同的嵌入方式，这些嵌入方式对仿射通用线性代数的分类表示。我们进一步提供了更自然的兼容性语句，以与量子Aggine Schur代数级别上的IDEMTOTENT版本嵌入。还建立了一个$ \ mathfrak {gl} _n $ - 嵌入的变量。
We establish an explicit embedding of a quantum affine $\mathfrak{sl}_n$ into a quantum affine $\mathfrak{sl}_{n+1}$. 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 affine $\mathfrak{sl}_n$ and $\mathfrak{gl}_n$. 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 $\mathfrak{gl}_n$-variant of the embedding is also established.
