Minuscule representations, invariant polynomials, and spectral covers

Details Minuscule representations, invariant polynomials, and spectral covers Minuscule representations, invariant polynomials, and spectral covers

2000-11-13

arxiv.org/abs/math/0011082v4

Mathematics

Algebraic Geometry

LaTeX, 42 pages, final version, to appear in the proceedings of the University of Missouri conference on Hilbert schemes, vect

Scientific paper

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.

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