Conformal Oscillator Representations of Orthogonal Lie Algebras

The conformal transformations with respect to the metric defining the orthogonal Lie algebra o(n) give rise to a one-parameter (c) family of inhomogeneous first-order differential operator representations of the orthogonal Lie algebra o(n+2). Letting these operators act on the space of exponential-polynomial functions that depend on a parametric vector a, we prove that the space forms an irreducible o(n+2)-module for any constant c if the vector a is not on a certain hypersurface. By partially swapping differential operators and multiplication operators, we obtain more general differential operator representations of o(n+2) on the polynomial algebra C in n variables. Moreover, we prove that the algebra C forms an infinite-dimensional irreducible weight o(n+2)-module with finite-dimensional weight subspaces if the constant c is not a half integer.Comment: 13page

Beam energy dependence of strange hadron production from STAR at RHIC

We present STAR measurements of K^{0}_{S}, \phi, \Lambda, \Xi, and \Omega at mid-rapidity from Au+Au collisions at \sqrt{s_{NN}} = 7.7, 11.5, 19.6, 27, and 39 GeV from the Beam Energy Scan (BES) program at the BNL Relativistic Heavy Ion Collider (RHIC). Nuclear modification factors and baryon-to-meson ratios are measured to understand recombination and parton energy loss mechanisms. Implications on partonic versus hadronic dynamics at low beam energies are discussed.Comment: 4 pages, 2 figures, Quark Matter 2012 proceeding