Proves Sagan-Swanson conjecture on monomial basis for SR_G of G = Z_r wr S_n and gives combinatorial model for its ungraded and exterior-graded G-module structure.
Diagonal supersymmetry for coinvariant rings
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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 $s_\lambda(\mathbf{q}/\mathbf{u})$ 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).
fields
math.CO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Calculates the bigraded Hilbert series of the GL_n(F_q)-superspace coinvariant ring SR = Omega/SI and gives an operator-theoretic characterization of SI^perp, extending to subgroups containing SL_n(F_q).
citing papers explorer
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Superspace coinvariants for wreath products
Proves Sagan-Swanson conjecture on monomial basis for SR_G of G = Z_r wr S_n and gives combinatorial model for its ungraded and exterior-graded G-module structure.
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Superspace coinvariants and inverse systems for $GL_n(\mathbb{F}_q)$
Calculates the bigraded Hilbert series of the GL_n(F_q)-superspace coinvariant ring SR = Omega/SI and gives an operator-theoretic characterization of SI^perp, extending to subgroups containing SL_n(F_q).