A skein relation for singular Soergel bimodules
| Autor: | Hogancamp, Matthew, Rose, David E. V., Wedrich, Paul |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the skein relation that governs the HOMFLYPT invariant of links colored by one-column Young diagrams. Our main result is a categorification of this colored skein relation. This takes the form of a homotopy equivalence between two one-sided twisted complexes constructed from Rickard complexes of singular Soergel bimodules associated to braided webs. Along the way, we prove a conjecture of Beliakova--Habiro relating the colored 2-strand full twist complex with the categorical ribbon element for quantum $\mathfrak{sl}_2$. Comment: 34 pages, many diagrams |
| Databáze: | arXiv |
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