2007/09/14 by Gerald W. Schwarz, Schwarz, Gerald W.
Mathematics · #20G20 #22E46 #22E60 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20G20 #msc:22E46 #msc:22E60
paper · pdf · doi:10.48550/arxiv.0709.2202
8 Pages, corrected theorems, more examples
openalex publication_date 2007/09/14 · arxiv created 2008/01/18 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G⊂\GL(V) be a complex reductive group where dim V<∞, and let π\colon V→\quot VG be the categorical quotient. Let \NN:=π\invπ(0) be the null cone of V, let H0 be the subgroup of \GL(V) which preserves the ideal \I of \NN and let H be a Levi subgroup of H0 containing G. We determine the identity component of H. In many cases we show that H=H0. For adjoint representations we have H=H0 and we determine H completely. We also investigate the subgroup GF of \GL(V) preserving a fiber F of π when V is an irreducible cofree G-module.