Gespeichert in:
| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2402.11368 |
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Inhaltsangabe:
- Leveraging skew Howe duality, we show that Lawson-Lipshitz-Sarkar's spectrification of Khovanov's arc algebra gives rise to 2-representations of categorified quantum groups over $\mathbb{F}_2$ that we call spectral 2-representations. These spectral 2-representations take values in the homotopy category of spectral bimodules over spectral categories. We view this as a step toward a higher representation theoretic interpretation of spectral enhancements in link homology. A technical innovation in our work is a streamlined approach to spectrifying arc algebras, using a set of canonical cobordisms that we call frames, that may be of independent interest. As a step towards extending these spectral 2-representations to integer coefficients, we also work in the $\mathfrak{gl}_2$ setting and lift the Blanchet-Khovanov algebra to a multifunctor into a multicategory version of Sarkar-Scaduto-Stoffregen's signed Burnside category.