Equivalence classes of subquotients of pseudodifferential operator modules

Consider the spaces of pseudodifferential operators between tensor density modules over the line as modules of the Lie algebra of vector fields on the line. We compute the equivalence classes of various subquotients of these modules. There is a 2-parameter family of subquotients with any given Jordan-Holder composition series. In the critical case of subquotients of length 5, the equivalence classes within each non-resonant 2-parameter family are specified by the intersections of a pencil of conics with a pencil of cubics. In the case of resonant subquotients of length 4 with self-dual composition series, as well as of lacunary subquotients of lengths 3 and 4, equivalence is specified by a single pencil of conics. Non-resonant subquotients of length exceeding 7 admit no non-obvious equivalences. The cases of lengths 6 and 7 are unresolved.

A Laboratory Search for a Long-Range T-odd, P-odd Interaction from Axion-Like Particles using Dual Species Nuclear Magnetic Resonance with Polarized Xe-129 and Xe-131 Gas

We place new limits on potential T- and P- violating monopole-dipole interactions between unpolarized nucleons and neutrons using dual species magnetic resonance in polarzed Xe gas. Free-induction decay transients with relaxation times ~20 s allow high precision measurements of the NMR frequencies, whose ratios cancel magnetic fluctuations. The new limits on the product gsgp improve on previous laboratory work by 2 orders of magnitude.