Differential graded Lie algebras and singularities of level sets of momentum mappings

The germ of an analytic varietyX at a pointxX is said to bequadratic if it is bi-analytically isomorphic to the germ of a cone defined by a system of homogeneous quadratic equations at the origin. Arms, Marsden and Moncrief show in [2] that under certain conditions the analytic germ of a level set of a momentum mapping is quadratic. We discuss related ideas in a more algebraic context by associating to an affine Hamiltonian action a differential graded Lie algebra, which in the presence of an invariant positive complex structure, is formal in the sence of [5].Dedicated to the memory of Bruce Reinhart     

Complete characterization of the (D2O)2 ground state: high Ka rotation-tunneling levels

We report the observation of extensive a- and c-type rotation-tunneling (RT) spectra of (D2O)2 for Ka = 0-4. These data allow quantification of molecular constants and tunneling splittings for a number of previously unobserved RT states of (D2O)2. The vibrational ground state has thus been characterized to energies as high as those of some of the intermolecular vibrations, and we present the first test of the VRT(ASP-W) potential at these high Ka states.