Séminaire Lotharingien de Combinatoire, 95B.12 (2026), 12 pp.
Robert Angarone, Patricia Commins, Trevor Karn, Satoshi Murai, Brendon Rhoades, and Andy Wilson
The Superspace Coinvariant Ring
Abstract.
Let F be a field of characteristic 0 and let
Ωn be the ring of regular differential forms
on Fn. The natural action
of Sn on Fn induces
an action on Ωn. The superspace coinvariant
ring is the quotient SRn of
Ωn by the ideal generated
by Sn-invariants with vanishing constant
term. We calculate the bigraded character of SRn,
describe a vector space basis of SRn, and give an
'operator theorem' which characterizes the associated inverse
system. Our results prove conjectures of Bergeron, Colmenarejo, Li,
Machacek, Reiner, Sagan, Sulzgruber, Swanson, Wallach, and Zabrocki.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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