Minuscule representations, invariant polynomials, and spectral covers

Given a minuscule representation of a simple Lie algebra, we find an algebraic model for the action of a regular element and show that these models can be glued together over the adjoint quotient, viewed as the set of all regular conjugacy classes of the Lie algebra. There are partial results in the case of a quasiminuscule representation, and a conjecture in the case of a general irreducible finite-dimensional representation. The method of proof is to relate the question to a problem concerning holomorphic principal bundles over cuspidal cubic curves.Comment: LaTeX, 42 pages, final version, to appear in the proceedings of the University of Missouri conference on Hilbert schemes, vector bundles and representation theory, new material on extensions and the adjoint representation of a simply laced Lie algebra adde

Implications of the r-mode instability of rotating relativistic stars

Several recent surprises appear dramatically to have improved the likelihood that the spin of rapidly rotating, newly formed neutron stars (and, possibly, of old stars spun up by accretion) is limited by a nonaxisymmetric instability driven by gravitational waves. Except for the earliest part of the spin-down, the axial l=m=2 mode (an r-mode) dominates the instability, and the emitted waves may be observable by detectors with the sensitivity of LIGO II. A review of these hopeful results is followed by a discussion of constraints on the instability set by dissipative mechanisms, including viscosity, nonlinear saturation, and energy loss to a magnetic field driven by differential rotation.Comment: 20 pages LaTeX2e (stylefile included), 6 eps figures. Review to appear in the proceedings of the 9th Marcel Grossman Meeting, World Scientific, ed. V. Gurzadyan, R. Jantzen, R. Ruffin