{"paper":{"title":"Vandermondes in superspace","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Timothy Wilson, Brendon Rhoades","submitted_at":"2019-06-07T20:00:21Z","abstract_excerpt":"Superspace of rank $n$ is a $\\mathbb{Q}$-algebra with $n$ commuting generators $x_1, \\dots, x_n$ and $n$ anticommuting generators $\\theta_1, \\dots, \\theta_n$. We present an extension of the Vandermonde determinant to superspace which depends on a sequence $\\mathbf{a} = (a_1, \\dots, a_r)$ of nonnegative integers of length $r \\leq n$. We use superspace Vandermondes to construct graded representations of the symmetric group. This construction recovers hook-shaped Tanisaki quotients, the coinvariant ring for the Delta Conjecture constructed by Haglund, Rhoades, and Shimozono, and a superspace quot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03315","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}