{"paper":{"title":"Superspace coinvariants for wreath products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendon Rhoades, Sutanay Bhattacharya","submitted_at":"2026-06-29T23:24:53Z","abstract_excerpt":"Let $\\Omega$ be the superspace ring of regular differential forms on the affine space $\\mathbb{C}^n$. If $G \\subseteq GL_n(\\mathbb{C})$ is a complex reflection group, the {\\em $G$-superspace coinvariant ring} is the quotient $SR_G := \\Omega_n/SI_G$ where $SI_G \\subseteq \\Omega$ is the ideal generated by $G$-invariants with vanishing constant term. We study this ring when $G = \\mathbb{Z}_r \\wr \\mathfrak{S}_n$ is the group of $r$-colored permutation matrices. We prove a conjecture of Sagan and Swanson on a monomial basis for $SR_G$ and give an Operator Theorem description of its inverse system. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30977","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/2606.30977/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"}