The international Symposium "Symmetries in Science X" was held at the Col- legium Mehrerau in Bregenz, Austria, during the period July 13-18, 1997. Some 40 invited scientists from 13 countries participated in the meeting. The Symposium was sponsored by the Technische Universitat Graz, the Land Vorarlberg, Austria, and the Landeshauptstadt Bregenz, Vorarlberg, Austria. I wish to thank Dr. Hubert Regner of the Amt der Vorarlberger Landesregierung, tlw Biirgermeister and Landtagsprasident Dipl. -Vw. Siegfried Gasser for financial assistence for the meeting, and Frater Albin Printschler of the Cloister Mehrerau for his continued support of the Symposium series. Bruno Gruber y CONTENTS Quantization on a Lie Group: Higher-Order Polarizations 1 V. Aldaya, J. Guerrero, and G. Marmo A Comparison between Algebraic Models of Molecular Spectroscopy 37 R. Bijker, A. Frank, R. Lemus, J. M. Arias, and F. Perez-Bernal On Disc:rete Media, Their Interaction Forms and the Origin of Non-Exactness of the Virtual Work ...47 E. Binz The k-Fermions and Objects Interpolating between Fermions and Bosons 63 M. Daoud, Y. Hassouni, and M.Kibler Polynomial Realization of the Uq(sl(3)) Gel'fand-(Weyl)-Zetlin Basis and Irregular Irreps at Roots of Unity ...79 V. K. Dobrev and R. Truini Nonstandard Deformation U~(son): The Imbedding U~(son) C Uq(sln) and Representations ...121 A. M. Gavrilik, N. Z. Iorgov, and A. U. Klimyk Algebraic: Methods in Physics 135 F. Iaehello Possible Origins of Quantum Fluctuations 145 M. Kanenaga and M.

The international Symposium "Symmetries in Science X" was held at the Col- legium Mehrerau in Bregenz, Austria, during the period July 13-18, 1997. Some 40 invited scientists from 13 countries participated in the meeting. The Symposium was sponsored by the Technische Universitat Graz, the Land Vorarlberg, Austria, and the Landeshauptstadt Bregenz, Vorarlberg, Austria. I wish to thank Dr. Hubert Regner of the Amt der Vorarlberger Landesregierung, tlw Biirgermeister and Landtagsprasident Dipl. -Vw. Siegfried Gasser for financial assistence for the meeting, and Frater Albin Printschler of the Cloister Mehrerau for his continued support of the Symposium series. Bruno Gruber y CONTENTS Quantization on a Lie Group: Higher-Order Polarizations 1 V. Aldaya, J. Guerrero, and G. Marmo A Comparison between Algebraic Models of Molecular Spectroscopy 37 R. Bijker, A. Frank, R. Lemus, J. M. Arias, and F. Perez-Bernal On Disc:rete Media, Their Interaction Forms and the Origin of Non-Exactness of the Virtual Work ...47 E. Binz The k-Fermions and Objects Interpolating between Fermions and Bosons 63 M. Daoud, Y. Hassouni, and M.Kibler Polynomial Realization of the Uq(sl(3)) Gel'fand-(Weyl)-Zetlin Basis and Irregular Irreps at Roots of Unity ...79 V. K. Dobrev and R. Truini Nonstandard Deformation U~(son): The Imbedding U~(son) C Uq(sln) and Representations ...121 A. M. Gavrilik, N. Z. Iorgov, and A. U. Klimyk Algebraic: Methods in Physics 135 F. Iaehello Possible Origins of Quantum Fluctuations 145 M. Kanenaga and M.