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 IX" was held at the Col- Mehrerau in Bregenz, Austria, during the period August 6-10, 1996. Some 40 legium invited scientists from 13 countries participated in the meeting. The Symposium was sponsored by Southern Illinois University at Carbondale, the Land Vorarlberg, Austria, and the Landeshauptstadt Bregenz, Vorarlberg, Austria. I wish to thank Chancellor Emeritus John C. Guyon of Southern Illinois Univer- sity at Carbondale, Dr. Hubert Regner of the Amt der Vorarlberger Landesregierung, and Biirgermeister and Landtagspriisident Dipl.-Vw. Siegfried Gasser for financial as- sistence for the meeting and Frater Albin Printschler of the Cloister Mehrerau for his continued support of the Symposium series. Bruno Gruber v CONTENTS Classical vs. Quantum Groups as Symmetries of Quantized Systems 1 M. Arik and C. Vnel Algebraic Model of an Oblate Top 9 R. Bijker and A. Leviatan The Mass-Squared Operator and the Einstein-Hilbert Action for Rescaled Lorentz Metrics ...25 E. Binz and P. Oellers Multichannel Dynamic Symmetry 37 J. Cseh Kazhdan-Lusztig Polynomials, Subsingular Vectors and Conditionally Invariant (q-Deformed) Equations ...47 V. K. Dobrev On a Path to Nonlinear QuantuIll Mechanics 81 H.-D. Doebner and J.-D. Hennig Quantum Mechanical Problems with q-Deformations and over the p-Adic Number Fields ...93 .

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."

Classical vs Quantum Groups as Symmetries of Quantized Systems; M. Arik, G. UEnel. Algebraic Model of an Oblate Top; R.Bijker, A. Leviatan. The Mass-Squared Operator and the Einstein-Hilbert Action for Rescaled Lorentz Metrics; E. Binz, P. Oellers. Multichannel Dynamic Symmetry; J. Cseh. Kazhdan-Lusztig Polynomials, Subsingular Vectors and Conditionally Invariant; q-Deformed Equations; V.K. Dobrev. On a Path to Nonlinear Quantum Mechanics; H.-D. Doebner, J.-D. Hennig. Quantum Mechanical Problems with q-Deformations and over the p-Adic Number Fields; I.H. Duru. A Symmetry Adapted Algebraic Approach to Molecular Spectroscopy; A. Frank, et al. Dyson Boson-Fermion Realization of Lie (Super)Algebras; D.V. Fursa, et al. Formal Languages for Quasicrystals; J.G. Escudero. On Quadratic and Nonquadratic Forms: Applications to R2m R2m-n Nonbijective Transformations; M. Kibler. Quantization of Systems with Constraints; J.R. Klauder. Automorphisms and Discrete Fiber Bundles; P. Kramer, et al. Algebraic Approach to Baryon Structure; A. Leviatan, R. Bijker. Discrete Reflection Groups and Induced Representations of Poincare Group on the Lattice; M. Lorente. 10 Additional Articles. Index.