## A New Class of Rotator Models for Statistical Mechanics and a Generalization of Lieb's Thereom |

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### Contents

Coherent representatives | 16 |

TV A generalized WignerEckart theorem | 32 |

0perator kernels for the angular momenta | 50 |

2 other sections not shown

### Common terms and phrases

A2Rn angular momenta appendix basic element basis bilinear characters classical partition function classical rotators coherent representatives compact components consequently coset da(a define denoted density matrix direct product direct sum eigenfunction eigenvalue element g equation equivalent evaluation g in G Grassmann manifold group elements Haar measure Hamiltonian harmonics of degree Hilbert space homogeneous polynomial homogeneous space identity operator implies infinitesimal behavior inner product integral representation invariant irreducible kernel functions kernel representative Lie algebra Lie group linear space linear transformation matrix elements momentum multiple n-dimensional n-dimensions N-tuple n-tuples of non-negative non-negative integers one-parameter subgroup operator kernel oriented two-planes orthogonal transformation orthonormal proper orthogonal transformation quantum partition function quantum spin r,s jr ks representation of G representation of S0n result right-hand side set of coherent spherical harmonics spin operators stationary subgroup subsets summands unit bivector unitary representations variables wedge representation Wigner-Eckart theorem yields