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

GUT baryogenesis after preheating: numerical study of the production and decay of X-bosons

We perform a fully non-linear calculation of the production of supermassive Grand Unified Theory (GUT) $X$ bosons during preheating, taking into account the fact that they are unstable with a decay width $\Gamma_X$. We show that parametric resonance does not develop if $\Gamma_X$ is larger than about $10^{-2} m_X$. We compute the nonthermal number density of superheavy bosons produced in the preheating phase and demonstrate that the observed baryon asymmetry may be explained by GUT baryogenesis after preheating if $\Gamma_X$ is smaller than about $10^{-3} m_X$.Comment: 13 pages, LaTeX file, 3 figures. One reference added and minor change

Photon decay in strong magnetic field in heavy-ion collisions

We calculate the photon pair production rate in strong magnetic field created in off-central heavy-ion collisions. Photon decay leads to depletion of the photon yield by a few percent at RHIC and by as much as 20% at the LHC. It also generates a substantial azimuthal asymmetry ("elliptic flow") of the final photon distribution. We estimate v_2~2% at RHIC and v_2~14% at LHC. Photon decay measurements is an important tool for studying the magnetic fields in early stages of heavy-ion collisions.Comment: 6 pages, 3 figure