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        "quote": "一个常见的混淆来源是：表示 $(\\pi,V)$ 有时简称为映射 $\\pi$，此时向量空间 $V$（即矩阵 $\\pi(g)$ 作用的空间）被省略；有时则直接指定空间 $V$，而省略映射 $\\pi$。这部分是因为 $\\pi$ 有时就是<span id=\"concept-1-identity-map\" class=\"block-anchor\"></span><u class=\"concept-term\" data-concept-id=\"concept-1-identity-map\" data-concept-role=\"discussion\" data-concept-identity=\"urn:uuid:67ac3c6c-23b7-46a9-b007-a83151e84721\" data-concept-route=\"/concept-identities#concept-67ac3c6c-23b7-46a9-b007-a83151e84721\" id=\"first-c103b1aa760687fcb609-zh\">恒等映射(identity map)</u>：例如，$G$ 常是 $GL(n,\\mathbf C)$ 的子群，也就是矩阵群，并通过矩阵对向量的标准作用作用于 $V\\simeq\\mathbf C^n$。不过，仅指定 $V$ 通常不足以确定表示，因为它未必是标准表示。例如，$V$ 上也可以取<span id=\"concept-1-trivial-representation\" class=\"block-anchor\"></span><u class=\"concept-term\" data-concept-id=\"concept-1-trivial-representation\" data-concept-role=\"discussion\" data-concept-identity=\"urn:uuid:811a9bef-7a24-4f51-a81e-f2924d9b3085\" data-concept-route=\"/concept-identities#concept-811a9bef-7a24-4f51-a81e-f2924d9b3085\" id=\"first-8c2a6cd4fa94ec5f9396-zh\">平凡表示(trivial representation)</u>，此时：",
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