{"paper":{"title":"Degenerate principal series of quantum Harish-Chandra modules","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Olga Bershtein","submitted_at":"2004-06-17T14:16:47Z","abstract_excerpt":"In this paper we study a quantum analogue of a degenerate principal series of $U_q \\mathfrak{su}_{n,n}$-modules ($0<q<1$) related to the Shilov boundary of the quantum $n \\times n$-matrix unit ball. We give necessary and sufficient conditions for the modules to be simple and unitarizable and investigate their equivalence.\n  These results are q-analogues of known classical results on reducibility and unitarizability of SU(n,n)-modules obtained by Johnson, Sahi, Zhang, Howe and Tan."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406343","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":""},"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"}