The representation theory of the exceptional Lie superalgebras F(4) and G(3)

This paper is a resolution of three related problems proposed by Yu. I. Manin and V. Kac for the so-called {\it{exceptional}} Lie superalgebras F(4) and G(3). The first problem posed by Kac (1978) is the problem of finding character and superdimension formulae for the simple modules. The second problem posed by Kac (1978) is the problem of classifying all indecomposable representations. The third problem posed by Manin (1981) is the problem of constructing the {\it{superanalogue}} of Borel-Weil-Bott theorem.Comment: 43 page

Free energy for non-equilibrium quasi-stationary states

We study a class of non-equilibrium quasi-stationary states for a Markov system interacting with two different thermal baths. We show that the work done under a slow, external change of parameters admits a potential, i.e., the free energy. Three conditions are needed for the existence of free energy in this non-equilibrium system: time-scale separation between variables of the system, partial controllability (external fields couple only with the slow variable), and an effective detailed balance. These conditions are facilitated in the continuous limit for the slow variable. In contrast to its equilibrium counterpart, the non-equilibrium free energy can increase with temperature. One example of this is that entropy reduction by means of external fields (cooling) can be easier (in the sense of the work cost) if it starts from a higher temperature.Comment: 8 pages, 2 figure

Production of Z^0 bosons with rapidity gaps: exclusive photoproduction in gamma p and p p collisions and inclusive double diffractive Z^0's

We extend the k_\perp-factorization formalism for exclusive photoproduction of vector mesons to the production of electroweak Z^0 bosons. Predictions for the gamma p \to Z^0 p and p p \to p p Z^0 reactions are given using an unintegrated gluon distribution tested against deep inelastic data. We present distributions in the Z^0 rapidity, transverse momentum of Z^0 as well as in relative azimuthal angle between outgoing protons. The contributions of different flavours are discussed. Absorption effects lower the cross section by a factor of 1.5-2, depending on the Z-boson rapidity. We also discuss the production of Z^0 bosons in central inclusive production. Here rapidity and (x_{\Pom,1}, x_{\Pom,2}) distributions of Z^0 are calculated. The corresponding cross section is about three orders of magnitude larger than that for the purely exclusive process.Comment: 19 pages, 14 figs, A. Cisek is married name of A. Rybarsk