{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:5d7e6d90-8fc4-4b2f-a97b-04bab6ff6e19", "labels": { "zh-CN": "对偶表示", "en": "dual representation" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "f6987a401a83cfc2b5e60da08f5154bbc03898fce8941f03c2f3c41a77ea8850", "occurrences": [ { "concept_id": "urn:uuid:5d7e6d90-8fc4-4b2f-a97b-04bab6ff6e19", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-04/02-dual-vector-spaces", "anchor": "first-9fcf711b7793bf89e6bc-zh", "chapter": "4", "section": "4.2", "offset": 6672, "range": [ 14694, 15014 ], "source_revision": "938d19d061a8b69c758beeb064276f3de2f0639a77ac963f124b6481149d29e7", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "对偶表示(dual representation)", "context": { "range": [ 14640, 15153 ], "quote": "对于群 $G$ 在 $V$ 上的任意表示 $( \\pi , V )$，我们可以在 $V^*$ 上定义相应的[对偶表示(dual representation)](../../../../../concepts/representation-theory/dual-representation)：\n", "quote_sha256": "2146c7c9ddef84cb98ef4a333f2da9689943074e731d60b02d668cbb7485a11c", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-04/02-dual-vector-spaces", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; 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not-concept-equivalence" } ], "id": "occ-bfc33afc2dedabf59625554b" }, { "concept_id": "urn:uuid:5d7e6d90-8fc4-4b2f-a97b-04bab6ff6e19", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-04/06-orthogonal-and-unitary-transformations", "anchor": "source-block-165", "chapter": "4", "section": "4.6", "offset": 4087, "range": [ 12961, 13246 ], "source_revision": "275772d36042626ed5283276e9f16090689e690c0c3bf42b24860f610c397103", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "对偶表示(dual representation)", "context": { "range": [ 12920, 13335 ], "quote": "回忆一下，群 $G$ 在 $V$ 上的表示 $\\pi$ 诱导出 $V^*$ 上的[对偶表示(dual representation)](../../../../../concepts/representation-theory/dual-representation)，其表示矩阵由 $\\pi$ 的转置逆给出。", "quote_sha256": "cf3a86707c53817ed79262a022692fd1860ab219ef2c330170a789976277f192", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-04/06-orthogonal-and-unitary-transformations", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; 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