Classical freeness of $\widehat{\mathfrak{sl}}_n$ at level $1$ via combinatorics

Shashank Kanade

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arXiv · 2606.19234

Classical freeness of $\widehat{\mathfrak{sl}}_n$ at level $1$ via combinatorics

Shashank Kanade

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Abstract

We use a family of Rogers--Ramanujan-type combinatorial identities of Dousse--Konan involving coloured partitions to prove classical freeness of the simple vertex operator algebras based on $\widehat{\mathfrak{sl}}_n$ at level $1$. These identities are used to produce Gröbner bases for the relevant arc algebras.

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Shashank Kanade. 2026-06-17. Classical freeness of $\widehat{\mathfrak{sl}}_n$ at level $1$ via combinatorics. https://arxiv.org/abs/2606.19234

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