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SUBGROUPS AND REPRESENTATIONS
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1-dimensional representations abelian antisymmetric atom belonging Brillouin zone carrier space Chapter character table coefficients column matrix commutator completely reduced contains corresponding cosets crystal defined Definition degeneracy diagonalizable dimension eigenvalues eigenvectors electrons energy eigenfunctions energy level equivalent Example finite follows group G group theory Hamiltonian Hence homogeneous Lorentz group homomorphism idempotent inequivalent integer irreducible components irreducible representation isomorphic Kronecker product lattice Let G Let us consider linearly independent little group Lorentz group matrix elements matrix group method molecular molecule normal coordinates normal subgroup obtain operators orbit orthogonality relations partition permutation Phys problem projective representation Quantum Mechanics quotient group representation of G second kind secular equation Sf(n solvable space group spin square matrix subduced subgroup H subgroup of G subspace symmetry coordinates symmetry group tensor Theorem Theory of Groups tion transformation unitary matrix wave equation wave functions Wigner zero