We define a limiting ${\mathfrak {sl}_N}$ Khovanov–Rozansky homology for semi-infinite positive multicolored braids. For a large class of such braids, we show that this limiting homology categorifies a highest-weight projector in the tensor product of fundamental representations determined by the coloring of the braid. This effectively completes the extension of Cautis’ similar result for infinite twist braids, begun in our earlier papers with Islambouli and Abel. We also present several similar results for other families of semi-infinite and bi-infinite multicolored braids.

中文翻译：

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无限多色辫子的 Khovanov-Rozansky 同源性

我们为半无限正多色辫子定义了一个极限 ${\mathfrak {sl}_N}$ Khovanov–Rozansky 同源性。对于一大类这样的辫子，我们证明了这种限制同源性在由辫子的颜色决定的基本表示的张量积中分类了最高权重的投影仪。这有效地完成了 Cautis 对无限扭曲辫子的类似结果的扩展，在我们早期与 Islambouli 和 Abel 的论文中开始。我们还为其他半无限和双无限多色辫子系列提供了几个类似的结果。