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The Bosonic-Fermionic Diagonal Coinvariant Modules Conjecture

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arxiv 2005.00924 v3 pith:OERYJCNK submitted 2020-05-02 math.CO math.RT

François Bergeron This is my paper
classification math.COmath.RT
keywords coinvariantconjecturediagonalmodulessetsvariablesanticommutingbosonic
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abstract

We describe a general conjecture on how one may derive from the generic bosonic case all structural properties of multivariate diagonal coinvariant modules in $k$ sets of $n$ commuting variables (bosons), and $j$ sets of $n$ anticommuting variables (fermions).

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A proof of the Fields Conjectures

    math.CO 2025-05 accept novelty 8.0 of 10

    The bigraded S_n-isomorphism type of the superspace coinvariant ring SR_n equals the sign-twisted permutation action on ordered set partitions, proving the Fields Conjectures.

  2. Diagonal supersymmetry for coinvariant rings

    math.CO 2025-05 accept novelty 7.0 of 10

    Coinvariant rings with k commuting and j anticommuting variables decompose into simple gl(k|j) representations, with universal super Schur function character formulas that do not depend on k and j.

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