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Groups Composed of Regular Matrices
Local Properties of Lie Groups
18 other sections not shown
5-functions A. O. Barut antisymmetric arbitrary basic representations calculation Cartan Cartan-Weyl Casimir invariants Casimir operator closed under commutation commutation relations components connected consider construct continuous corresponding coupling coefficients covering group defined degeneracy diagonal dimensional discrete dynamical group Dynkin diagram eigenvalues eigenvectors elementary representations Euclidean group Euclidean space evaluation EXERCISES fermion finite group functions give given greatest weight group elements group G harmonic oscillator harmonic-oscillator hence highest weight hydrogen atom identity element infinitesimal operators integers irreducible representation isoscalar factors Kronecker product labeled Lie algebra associated Lie group linear combination mass spectrum neighborhood noncompact group nonunitary obtain orthogonal parameters phase Phys plethysm properties quantum numbers quasi-spin readily real line recoupling reduced matrix elements result root vectors satisfy semisimple Lie algebra shell Show simple Lie algebras simple roots simply reducible spinor representations subalgebra subgroup subspace symmetric symplectic Table tensor operator tions topological group topological space transformation unitary representations Wigner-Eckart theorem