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 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 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 .