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Minimal W-algebras of mathfrak{so}_N at level minus one

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arxiv 2506.15605 v1 pith:BQFJAEO6 submitted 2025-06-18 math.RT math.QA

Minimal W-algebras of mathfrak{so}_N at level minus one

Thomas Creutzig , Justine Fasquel , Vladimir Kovalchuk , Andrew R. Linshaw , Shigenori Nakatsuka This is my paper
classification math.RT math.QA
keywords levelmathfrakminimalalgebraevenmathcalminussimple
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For $N \in\mathbb Z_{\geq 7}$ we show that the simple minimal $\mathcal{W}$-algebra of $\mathfrak{so}_N$ at level minus one is isomorphic to the even subalgebra of the tensor product of the simple affine vertex superalgebra of $\mathfrak{osp}_{1|2}$ at level $\frac{N-6}{2}$ with $N-4$ free fermions. In particular when $N$ is even this minimal $\mathcal{W}$-algebra is strongly rational as conjectured by Arakawa-Moreau.

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    math.RT 2026-04 unverdicted novelty 8.0

    The universal N=2 supersymmetric W_infty algebra exists as a 2-parameter family whose Y-algebra quotients satisfy the conjectured dualities, giving coset realizations and strong rationality for W_k(sl_{n+1|n}) at k = ...