A Quotient Restriction Theorem for actions of real reductive groups

2008/11/26 by Henrik Stoetzel, Stoetzel, Henrik
Mathematics · #22E46 #53D20 #57S20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:22E46 #msc:53D20 #msc:57S20

paper · pdf · doi:10.48550/arxiv.0811.4273

14 pages

arxiv created 2008/11/26 · openalex publication_date 2008/11/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a version of the Chevalley Restriction Theorem for the action of a real reductive group G on a topological space X which locally embeds into a holomorphic representation. Assuming that there exists an appropriate quotient X//G for the G-action, we introduce a stratification which is defined with respect to orbit types of closed orbits. Our main result is a description of the quotient X//G in terms of quotients by normalizer subgroups associated to the stratification.

Citations

• Convexity properties of gradient maps

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