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October 20, 2025Open Access

Diagonal Supersymmetry for Coinvariant Rings

Key Points

The study proves that bosonic-fermionic coinvariant rings have a natural module structure related to groups.
Its findings include the character series being a sum of super Schur functions multiplied by characters of G.
In particular, this work confirms the Diagonal Supersymmetry conjecture for symmetric groups, adding theoretical insights.
Key structures and relationships observed throughout remain independent of the parameters k and j, enhancing their universality.

Abstract

For finite groups G, we show that bosonic-fermionic coinvariant rings have a natural U (gl (k|j) ) CG-module structure. In particular, we show that their character series are a sum of super Schur functions s_ (q/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 Bergeron (2020).

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Cite This Study

John Lentfer (Tue,) studied this question.

synapsesocial.com/papers/68f5a78aab63786de5b460d9 https://doi.org/https://doi.org/10.48550/arxiv.2505.14885

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