Séminaire Lotharingien de Combinatoire, 95B.87 (2026), 12 pp.
John Lentfer
Diagonal Supersymmetry for Coinvariant Rings
Abstract.
For finite groups G, we show that bosonic-fermionic coinvariant
rings have a natural U(gl(k|j))
⊗ C[G]-module structure.
In particular, we show that their character series are sums of super
Schur functions sλ(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 F. Bergeron (2020).
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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