{"paper":{"title":"Contractive Hilbert modules on quotient domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"E. K. Narayanan, Gargi Ghosh, Shibananda Biswas, Subrata Shyam Roy","submitted_at":"2024-09-17T11:54:15Z","abstract_excerpt":"Let the complex reflection group $G(m,p,n)$ act on the unit polydisc $\\mathbb D^n$ in $\\mathbb C^n.$ A $\\boldsymbol\\Theta_n$-contraction is a commuting tuple of operators on a Hilbert space having $$\\overline{\\boldsymbol\\Theta}_n:=\\{\\boldsymbol\\theta(z)=(\\theta_1(z),\\ldots,\\theta_n(z)):z\\in\\overline{\\mathbb D}^n\\}$$ as a spectral set, where $\\{\\theta_i\\}_{i=1}^n$ is a homogeneous system of parameters associated to $G(m,p,n).$ A plethora of examples of $\\boldsymbol\\Theta_n$-contractions is exhibited. Under a mild hypothesis, it is shown that these $\\boldsymbol\\Theta_n$-contractions are mutually"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.11101","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/2409.11101/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"}