theorem A.354 Harish-Chandra, quoted: the labels separate

Rests on

• depends_on corollary 14.18 A Casimir acts as a number on an irreducible representation ¶
  • depends_on definition 14.8 Casimir element ¶
    • depends_on definition 14.5 Universal enveloping algebra ¶
      • depends_on equation 14.5 eq:lie-structconst ¶
        • step_from equation 14.4 eq:lie-gengrlie ¶
  • depends_on equation 14.6 eq:lie-expgen ¶
  • depends_on remark 14.6 What $U(\mathfrak{g})$ is for ¶
  • depends_on theorem 5.158 Schur's first lemma ¶
    • depends_on definition 5.37 Linear transformation ¶
      • depends_on definition 4.33 Vector space ¶
        • depends_on definition 4.8 Commutativity; abelian structure ¶
        • depends_on definition 4.32 Field ¶
        • depends_on definition 4.31 Module ¶
    • depends_on definition 5.147 Invariant subspace ¶
      • depends_on definition 5.7 Vector subspace ¶
        • depends_on definition 5.5 Linear combination ¶
      • depends_on definition 5.141 Representation of a group ¶
        • depends_on definition 4.21 Group ¶
        • depends_on definition 4.43 Group homomorphism ¶
        • depends_on definition 4.48 Symmetric group ¶
    • depends_on definition 5.148 Irreducible representation ¶
      • depends_on definition 5.147 Invariant subspace ¶ ↺
    • proves proof ch:03-linear-algebra-representations@proof-67 ¶
  • proves proof ch:12-lie-groups-fibre-bundles@proof-6 ¶
• depends_on definition 14.8 Casimir element ¶ ↺

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