Generic super-orbits in gl(m|n)* and their braided counterparts

We introduce some braided varieties -- braided orbits -- by considering quotients of the so-called Reflection Equation Algebras associated with Hecke symmetries (i.e. special type solutions of the quantum Yang-Baxter equation). Such a braided variety is called regular if there exists a projective module on it, which is a counterpart of the cotangent bundle on a generic orbit O in gl(m)* in the framework of the Serre approach. We give a criterium of regularity of a braided orbit in terms of roots of the Cayley-Hamilton identity valid for the generating matrix of the Reflection Equation Algebra in question. By specializing our general construction we get super-orbits in gl(m|n)* and a criterium of their regularity

Gamma Radiation by Neutralino Stars

A new model of gamma radiation (GR) generated by neutralino annihilation in neutralino stars (NeS) is proposed. Diffuse Galactic and extragalactic GR is calculated for this model and is shown to be in a reasonable agreement with observations. The point source component (P) is picked out among nonidentified discrete gamma sources from EGRET catalog. This component is shown to be distributed isotropically and homogeneously, as it should be for NeS. Gamma radiation from significant part of P-sources is supposed to be the direct radiation from individual NeS. This supposition is shown to be in agreement with observations. The comparison of the theory with observed GR gives a possibility to establish some important features of CDM particle.Comment: 12 pages, LaTe

Braided Differential Operators on Quantum Algebras

We define the braided differential algebras which can be interpreted as quantization of the differential operator algebra defined on some algebraic varieties supplied with the action of the group GL(m). The algebra is generated by right invariant or coajoint vector fields. Our main example is gl^*(m) and coadjoint orbits in it. The Heisenberg double on the quantum group Fun_q(GL(m)is a particular case of the suggested construction.Comment: Corrected and extended version. An illustrative example is added into the Section 5. LaTex file, 24 pp. Accepted for publication in "Journal of Geometry and Physics

Double quantization of \cp type orbits by generalized Verma modules

It is known that symmetric orbits in ${\bf g}^*$ for any simple Lie algebra ${\bf g}$ are equiped with a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the reduced Sklyanin bracket associated to the "canonical" R-matrix. We realize quantization of this Poisson pencil on \cp type orbits (i.e. orbits in $sl(n+1)^*$ whose real compact form is $CP^n$) by means of q-deformed Verma modules.Comment: 21 pages, LaTeX, no figure

On Whitham theory for perturbed integrable equations

Whitham theory of modulations is developed for periodic waves described by nonlinear wave equations integrable by the inverse scattering transform method associated with $2\times2$ matrix or second order scalar spectral problems. The theory is illustrated by derivation of the Whitham equations for perturbed Korteweg-de Vries equation and nonlinear Schr\"odinger equation with linear damping.Comment: 17 pages, no figure

Braided Weyl algebras and differential calculus on U(u(2))

On any Reflection Equation algebra corresponding to a skew-invertible Hecke symmetry (i.e. a special type solution of the Quantum Yang-Baxter Equation) we define analogs of the partial derivatives. Together with elements of the initial Reflection Equation algebra they generate a "braided analog" of the Weyl algebra. When $q\to 1$, the braided Weyl algebra corresponding to the Quantum Group $U_q(sl(2))$ goes to the Weyl algebra defined on the algebra \Sym((u(2)) or that $U(u(2))$ depending on the way of passing to the limit. Thus, we define partial derivatives on the algebra $U(u(2))$, find their "eigenfunctions", and introduce an analog of the Laplace operator on this algebra. Also, we define the "radial part" of this operator, express it in terms of "quantum eigenvalues", and sketch an analog of the de Rham complex on the algebra $U(u(2))$. Eventual applications of our approach are discussed.Comment: LaTex, 18 pages. Accepted in Journal of Geometry and Physic

Experimental Evidence of Giant Electron - Gamma Bursts Generated by Extensive Atmospheric Showers in Thunderclouds

The existence of a new phenomena - giant electron-gamma bursts is established. The bursts are generated in thunderclouds as a result of the combined action of runaway breakdown and extensive atmosphere showers (RB-EAS). The experiments were fulfilled at the Tien Shan Mountain Scientific Station using EAS-Radio installation. This specially constructed installation consists of a wide spread EAS trigger array and a high time resolution radiointerferometer.Comment: 30 pages, 16 figure