{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:9e24a1e3-d6ef-4cdf-8871-7731a246b44d",
  "labels": {
    "zh-CN": "子表示",
    "en": "subrepresentation"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "da3229806b35c23c78b7be9177ec54553e2579564a6514d26980b5d8c762412b",
  "occurrences": [
    {
      "concept_id": "urn:uuid:9e24a1e3-d6ef-4cdf-8871-7731a246b44d",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-04/04-introduction-to-group-representation-theory",
      "anchor": "concept-4-subrepresentation",
      "chapter": "4",
      "section": "4.4",
      "offset": 3498,
      "range": [
        8596,
        8835
      ],
      "source_revision": "8659a22bf0394df6e0f0547cc91ed5a8dd18c3b22a3aa2463bbac9fbfc4f313c",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "子表示(subrepresentation)",
      "context": {
        "range": [
          8424,
          9197
        ],
        "quote": "对每个 $g \\in G$，映射 $T ( g )$ 是满射，$T ( g ) W = W$，因为对每个向量 $w \\in W$ 都有 $w = T ( g ) ( T ( g ^ { - 1 } w ) )$。因此，$T ( g )$ 在 $W$ 上的限制是 $W$ 的一个自同构，并给出 $G ,$ 的另一个表示，称为 $G ,$ 的一个 <u id=\"concept-4-subrepresentation\" class=\"concept-term\" data-concept-identity=\"urn:uuid:9e24a1e3-d6ef-4cdf-8871-7731a246b44d\" data-concept-route=\"/concept-identities#concept-9e24a1e3-d6ef-4cdf-8871-7731a246b44d\">子表示(subrepresentation)</u>，记作 $T _ { W }$ $G \\to G L ( W )$。整个空间 $V$ 与平凡子空间 0 显然对 $V$ 上的任意表示 $T$ 都是 $G$-不变的。若这些是仅有的不变子空间，则称该表示是 <u id=\"concept-4-irreducible-representation\" class=\"concept-term\" data-concept-identity=\"urn:uuid:4e9e2c89-0422-42cf-8762-6b5e59837ef0\" data-concept-route=\"/concept-identities#concept-4e9e2c89-0422-42cf-8762-6b5e59837ef0\">不可约表示(irreducible representation)</u>。",
        "quote_sha256": "bd703466f30c5a0859bfd1f8d5095fccec33febcd690da3b05e5fe7618c78ac7",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-04/04-introduction-to-group-representation-theory",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-b26023fe4a7076d732942d47"
    }
  ],
  "registered_positions": [
    {
      "route": "zh/chapter-04/04-introduction-to-group-representation-theory",
      "lang": "zh-CN",
      "section": "4.4",
      "signal": "term-mark",
      "label": "子表示",
      "english": "subrepresentation",
      "offset": 2718
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-b26023fe4a7076d732942d47"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 1,
    "located_occurrences": 1,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "593041effba973d8888141312fe0f08bbdeaed0f7376a5ec5007e9d7cf7a8403",
  "optional_enrichments": []
}
