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Khovanov–Rozansky homology for infinite multicolored braids
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AbstractWe 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.
Title: Khovanov–Rozansky homology for infinite multicolored braids
Description:
AbstractWe 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.
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