Representations With a Reduced Null Cone
Algebraic Geometry
2011-12-16 v1 Commutative Algebra
Representation Theory
Abstract
Let G be a complex reductive group and V a G-module. Let \pi: V \to V//G be the quotient morphism and set N(V) = \pi^{-1}(\pi(0)). We consider the following question. Is the null cone N(V) reduced, i.e., is the ideal of N(V) generated by G-invariant polynomials? We have complete results when G is SL_2, SL_3 or a simple group of adjoint type, and also when G is semisimple of adjoint type and the G-module V is irreducible.
Keywords
Cite
@article{arxiv.1112.3634,
title = {Representations With a Reduced Null Cone},
author = {Hanspeter Kraft and Gerald W. Schwarz},
journal= {arXiv preprint arXiv:1112.3634},
year = {2011}
}