Web演算和倾斜模块类型$C_2$

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-09-29 DOI:10.4171/qt/166

Elijah Bodish

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引用次数: 8

摘要

利用Kuperberg的$B_2/C_2$网，在Elias和Libedinsky的基础上，我们描述了一个“轻叶”算法来构造$\mathfrak{so}_5\cong \mathfrak{sp}_4$(及其相关量子群)的基本表示的任意张量积之间的态射基。我们的论证很少依赖于基本场。结果证明了当$[2]_q\ne 0$时，$C_2$ web范畴的Karoubi包络等价于分幂量子群$\mathcal{U}_q^{\mathbb{Z}}(\mathfrak{sp}_4)$的倾斜模范畴。

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Web calculus and tilting modules in type $C_2$

Using Kuperberg's $B_2/C_2$ webs, and following Elias and Libedinsky, we describe a "light leaves" algorithm to construct a basis of morphisms between arbitrary tensor products of fundamental representations for $\mathfrak{so}_5\cong \mathfrak{sp}_4$ (and the associated quantum group). Our argument has very little dependence on the base field. As a result, we prove that when $[2]_q\ne 0$, the Karoubi envelope of the $C_2$ web category is equivalent to the category of tilting modules for the divided powers quantum group $\mathcal{U}_q^{\mathbb{Z}}(\mathfrak{sp}_4)$.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.