{"paper":{"title":"Superspace coinvariants and inverse systems for $GL_n(\\mathbb{F}_q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andy Wilson, Brendon Rhoades","submitted_at":"2026-06-10T01:16:45Z","abstract_excerpt":"Let $q$ be a prime power and write $\\Omega$ for the bigraded algebra of regular differential forms over $\\mathbb{F}_q^n$. The general linear group $GL_n(\\mathbb{F}_q)$ acts on $\\Omega$; write $SI \\subseteq \\Omega$ for the ideal generated by $GL_n(\\mathbb{F}_q)$-invariants with vanishing constant term. The {\\em $GL_n(\\mathbb{F}_q)$-superspace coinvariant ring} is the quotient $SR := \\Omega/SI$. We calculate the bigraded Hilbert series of $SR$ and give an operator-theoretic characterization of the inverse system $SI^\\perp$. Our results extend to subgroups $G$ of $GL_n(\\mathbb{F}_q)$ which contai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11549","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11549/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}