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Invariant meromorphic functions on Stein spaces

Daniel Greb, Christian Miebach (2012)

Annales de l’institut Fourier

In this paper we develop fundamental tools and methods to study meromorphic functions in an equivariant setup. As our main result we construct quotients of Rosenlicht-type for Stein spaces acted upon holomorphically by complex-reductive Lie groups and their algebraic subgroups. In particular, we show that in this setup invariant meromorphic functions separate orbits in general position. Applications to almost homogeneous spaces and principal orbit types are given. Furthermore, we use the main result...

Invariants d'un sous-groupe unipotent maximal d'un groupe semi-simple

Michel Brion (1983)

Annales de l'institut Fourier

Soit G un groupe algébrique semi-simple complexe, U un sous-groupe unipotent maximal de G , T un tore maximal de G normalisant U . Si V est un G -module rationnel de dimension finie, alors G opère sur l’algèbre C [ V ] des fonctions polynomiales sur V ; la structure de G -module de C [ V ] est décrite par la T -algèbre C [ V ] U des U -invariants de C [ V ] . Cette algèbre est de type fini et multigraduée (par le degré de C [ V ] et le poids par rapport à T ). On donne une formule intégrale pour la série de Poincaré de cette algèbre graduée....

Invariants of four subspaces

Gerry W. Schwarz, David L. Wehlau (1998)

Annales de l'institut Fourier

We consider problems in invariant theory related to the classification of four vector subspaces of an n -dimensional complex vector space. We use castling techniques to quickly recover results of Howe and Huang on invariants. We further obtain information about principal isotropy groups, equidimensionality and the modules of covariants.

Is the Luna stratification intrinsic?

Jochen Kuttler, Zinovy Reichstein (2008)

Annales de l’institut Fourier

Let G → GL ( V ) be a representation of a reductive linear algebraic group G on a finite-dimensional vector space V , defined over an algebraically closed field of characteristic zero. The categorical quotient X = V // G carries a natural stratification, due to D. Luna. This paper addresses the following questions:(i) Is the Luna stratification of X intrinsic? That is, does every automorphism of V // G map each stratum to another stratum?(ii) Are the individual Luna strata in X intrinsic? That is, does every automorphism...

Lectures on spherical and wonderful varieties

Guido Pezzini (2010)

Les cours du CIRM

These notes contain an introduction to the theory of spherical and wonderful varieties. We describe the Luna-Vust theory of embeddings of spherical homogeneous spaces, and explain how wonderful varieties fit in the theory.

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