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arXiv · 2408.13785

Connecting affine $\mathcal{W}$-algebras: A case study on $\mathfrak{sl}_4$

Justine Fasquel·Zachary Fehily·Ethan Fursman·Shigenori Nakatsuka
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Abstract

We introduce the partial reductions and inverse Hamiltonian reductions between affine $\mathcal{W}$-algebras along the closure relations of associated nilpotent orbits in the case of $\mathfrak{sl}_4$, fulfilling all the missing constructions in the literature. We also apply the partial reductions to modules in the Kazhdan-Lusztig category and show compatibility with the usual reductions of Weyl modules.

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Justine Fasquel, Zachary Fehily, Ethan Fursman, Shigenori Nakatsuka. 2024-08-25. Connecting affine $\mathcal{W}$-algebras: A case study on $\mathfrak{sl}_4$. https://doi.org/10.1016/j.jpaa.2025.108149

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