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arXiv · 2505.14885

Diagonal supersymmetry for coinvariant rings

John Lentfer
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Abstract

For finite groups $G$, we show that bosonic-fermionic coinvariant rings have a natural $U(\mathfrak{gl}(k|j)) \otimes \mathbb{C}[G]$-module structure. In particular, we show that their character series are sums of super Schur functions $s_λ(\mathbf{q}/\mathbf{u})$ times irreducible characters of $G$ with universal coefficients, which do not depend on $k,j$. In the case where $G$ is the symmetric group with diagonal action, this proves the "Diagonal Supersymmetry" conjecture of F. Bergeron (2020).

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John Lentfer. 2026-06-23. Diagonal supersymmetry for coinvariant rings. https://arxiv.org/abs/2505.14885

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