{"paper":{"title":"Reducing sub-modules of the Bergman module $\\mathbb A^{(\\lambda)}(\\mathbb D^n)$ under the action of the symmetric group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gadadhar Misra, Gargi Ghosh, Shibananda Biswas, Subrata Shyam Roy","submitted_at":"2017-07-10T17:28:05Z","abstract_excerpt":"The weighted Bergman spaces on the polydisc, $\\mathbb A^{(\\lambda)}(\\mathbb D^n)$, $\\lambda>0,$ splits into orthogonal direct sum of subspaces $\\mathbb P_{\\boldsymbol p}\\big(\\mathbb A^{(\\lambda)}(\\mathbb D^n)\\big)$ indexed by the partitions $\\boldsymbol p$ of $n,$ which are in one to one correspondence with the equivalence classes of the irreducible representations of the symmetric group on $n$ symbols. In this paper, we prove that each sub-module $\\mathbb P_{\\boldsymbol p}\\big(\\mathbb A^{(\\lambda)}(\\mathbb D^n)\\big)$ is a locally free Hilbert module of rank equal to square of the dimension $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02956","kind":"arxiv","version":2},"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"}