In this paper, we define an explicit basis for the [Formula: see text]-web algebra [Formula: see text] (the [Formula: see text] generalization of Khovanov’s arc algebra) using categorified [Formula: see text]-skew Howe duality.Our construction is a [Formula: see text]-web version of Hu–Mathas’ graded cellular basis and has two major applications: it gives rise to an explicit isomorphism between a certain idempotent truncation of a thick calculus cyclotomic KLR algebra and [Formula: see text], and it gives an explicit graded cellular basis of the [Formula: see text]-hom space between two [Formula: see text]-webs. We use this to give a (in principle) computable version of colored Khovanov–Rozansky [Formula: see text]-link homology, obtained from a complex defined purely combinatorially via the (thick cyclotomic) KLR algebra and needs only [Formula: see text].

中文翻译：

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𝔤𝔩n-webs、分类和 Khovanov-Rozansky 同调

在本文中，我们使用分类 [Formula: see text]-skew 为 [Formula: see text]-web algebra [Formula: see text]（Khovanov 弧代数的 [Formula: see text] 泛化）定义了一个明确的基础Howe duality. 我们的构造是 Hu-Mathas 分级细胞基础的 [公式：见文本]-web 版本，有两个主要应用：它在厚微积分分圆 KLR 代数的某个幂等截断和[公式：见正文]，它给出了两个 [公式：见正文]-网之间的 [公式：见正文]-hom 空间的明确分级细胞基础。我们使用它来给出（原则上）有色 Khovanov–Rozansky [公式：见文本]-链接同源性的可计算版本，从通过（厚分圆）KLR 代数纯粹组合定义的复数获得，并且只需要 [公式：