Homogeneous right coideal subalgebras of quantized enveloping algebras

For a quantized enveloping algebra of a complex semisimple Lie algebra with deformation parameter not a root of unity, we classify all homogeneous right coideal subalgebras. Any such right coideal subalgebra is determined uniquely by a triple consisting of two elements of the Weyl group and a subset of the set of simple roots satisfying some natural conditions. The essential ingredients of the proof are the Lusztig automorphisms and the classification of homogeneous right coideal subalgebras of the Borel Hopf subalgebras of quantized enveloping algebras obtained previously by H.-J. Schneider and the first named author. Key words: Quantum groups, coideal subalgebras, Weyl group, weak orderComment: 13 page

Podle\'s' Quantum Sphere: Dual Coalgebra and Classification of Covariant First Order Differential Calculus

The dual coalgebra of Podle\'s' quantum sphere O_q(S^2_c) is determined explicitly. This result is used to classify all finite dimensional covariant first order differential calculi over O_q(S^2_c) for all but exceptional values of the parameter c.Comment: LaTeX2e, 19 page

Discovery of Long-Lived Shape Isomeric States which Decay by Strongly Retarded High-Energy Particle Radioactivity

The reaction 28Si + 181Ta has been studied at E(Lab) = 125 and 135 MeV. Coincidences between high energy particles and various X- and gamma-rays from abnormally long-lived states were observed. e.g. 7.8 - 8.6 MeV alpha-particles with gamma-rays of a superdeformed band, 5.1 - 5.5 MeV alpha-particles with X- and gamma-rays of W, Re, and Pt, and 3.88 MeV particles (interpreted as protons) with 185.8 keV gamma-rays. The data are interpreted in terms of the production of long-lived (t(1/2) of several months) high spin isomeric states in the second well of the potential in the parent nuclei, which decay to the normal states in the daughters, and in the third well of the potential, which decay to the second well.Comment: 25 pages including 11 figures and 3 table