Diffraction 2000: New Scaling Laws in Shadow Dynamics

New scaling structure for the shadow corrections in elastic scattering from deuteron at high energies has been presented and discussed. It is shown that this structure corresponds to the experimental data on proton(antiproton)-deuteron total cross sections. The effect of weakening for the inelastic screening at superhigh energies has been theoretically predicted.Comment: LaTex2e, espcrc2.sty, 2 figures, Contribution to the Workshop "Diffraction 2000", Cetraro, Ialy, Sept. 2-7, 2000, to be published in proceedings of the Worksho

Semiinfinite cohomology of contragradient Weyl modules over small quantum groups

In this paper we construct some quantum analogues of the global Cousin complex for the flag variety in positive characteristic. Just like in the positive characteristic case, we obtain some remarkable resolutions of the contragradient modules over the small quantum group. We use these resolutions to calculate semiinfinite cohomology of the small quantum group with coefficients in contragradient Weyl modules. It turns out that the described graded space of semiinfinite cohomology is naturally isomorphic to the space of distributions on the cotangent bundle of the flag variety with support in the union of conormal bundles to the Schubert cells with coefficients in the pull-back of a line bundle on the flag variety.Comment: 20 pages, AMSLaTe

Semiinfinite cohomology of quantum groups

In this paper we develop a new homology theory of associative algebras called semiinfinite cohomology in a derived category setting. We show that in the case of small quantum groups the zeroth semiinfinite cohomology of the trivial module is closely related to the conformal blocks' spaces. We provide a description of the semiinfinite cohomology spaces of the trivial module over a small quantum group in terms of distributions on the nilpotent cone of the corresponding semisimple Lie algebra.Comment: 24 page