remark 14.6 What $U(\mathfrak{g})$ is for

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Supports

• depends_on corollary 14.18 A Casimir acts as a number on an irreducible representation ¶
  • depends_on proposition 14.55 The fundamental, the antifundamental and the adjoint ¶
    • depends_on corollary A.377 The adjoint representation is irreducible ¶
    • depends_on example A.358 Rank two: $\mathfrak{su}(3)$ ¶
    • depends_on theorem 14.57 $\vect{3}\otimes\bar{\vect{3}} = \vect{1}\oplus\vect{8}$ ¶
      • depends_on proposition 102.6 Mesons are $q\bar{q}$, baryons are $qqq$ ¶
        • assumes experiment Deep Inelastic Scattering ¶
        • depends_on phenomenon 116.38 The quark spins do not account for the proton spin ¶
        • depends_on phenomenon 102.9 The $\Delta^{++}$ violates the spin-statistics theorem ¶
        • depends_on phenomenon 102.7 The nucleon magnetic moments come out right ¶
        • depends_on proposition 116.29 The Gross–Llewellyn Smith sum rule in the parton model ¶
    • depends_on theorem 102.12 Which quark combinations can be colour singlets ¶
      • depends_on corollary 102.13 The selection rule of the eightfold way ¶
  • depends_on theorem A.354 Harish-Chandra, quoted: the labels separate ¶