Action on flag varieties: 2-Dimensional case

LetA be a finite dimensional commutative semisimple algebra over a fieldk and letV be a finitely generatedA-module. We examine the action of the general linear group GL _A (V) on the set of flags ofk-subspaces ofV. Also, let (V, B) be a finitely generated symplectic module overA. We also investigate the action of the symplectic group Sp _A (V, B) on the set of flags ofB-isotropick-subspaces ofV, whereB=°B is thek-symplectic form induced by a nonzerok-linear map :A k. In both cases, the orbits are completely classified in terms of certain integer invariants provided that dim _{k A}=2.This work is partially supported by a KOSEF research grant.     

Condensed matter effects on nuclear fusion rates in laboratory and astrophysical environments

Previously overlooked condensed matter effects (CME) can significantly influence nuclear fusion rates in both laboratory and astrophysical environments. In dense plasmas, the ensemble of fusing particles has a significant exchange of kinetic and potential energies. Thus, there are diminished effective flux velocities resulting in a significant selective reduction of fusion rates. Our CME predictions are testable in laboratory experiments and have broad-ranging implications on the fusion rates for stellar media in general. By calculating reaction rates forp(p, e ⁺ v _e ) D and⁷Be(p, )⁸B in the sun, we show that CME help to solve the solar neutrino problem.