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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.

Linear bounds for levels of stable rationality

Fedor Bogomolov, Christian Böhning, Hans-Christian Graf von Bothmer (2012)

Open Mathematics

Let G be one of the groups SLn(ℂ), Sp2n (ℂ), SOm(ℂ), Om(ℂ), or G 2. For a generically free G-representation V, we say that N is a level of stable rationality for V/G if V/G × ℙN is rational. In this paper we improve known bounds for the levels of stable rationality for the quotients V/G. In particular, their growth as functions of the rank of the group is linear for G being one of the classical groups.

Moduli spaces of local systems and higher Teichmüller theory

Vladimir Fock, Alexander Goncharov (2006)

Publications Mathématiques de l'IHÉS

Let G be a split semisimple algebraic group over Q with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S to G(R), construct explicitly all positive representations, and prove that they are faithful, discrete, and positive hyperbolic; the moduli space of positive representations is a topologically trivial open domain in the space of all representations. When S have holes, we defined two moduli spaces closely...

On classical invariant theory and binary cubics

Gerald W. Schwarz (1987)

Annales de l'institut Fourier

Let G be a reductive complex algebraic group, and let C [ m V ] G denote the algebra of invariant polynomial functions on the direct sum of m copies of the representations space V of G . There is a smallest integer n = n ( V ) such that generators and relations of C [ m V ] G can be obtained from those of C [ n V ] G by polarization and restitution for all m > n . We bound and the degrees of generators and relations of C [ n V ] G , extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics.

On deformation method in invariant theory

Dmitri Panyushev (1997)

Annales de l'institut Fourier

In this paper we relate the deformation method in invariant theory to spherical subgroups. Let G be a reductive group, Z an affine G -variety and H ⊂ G a spherical subgroup. We show that whenever G / H is affine and its semigroup of weights is saturated, the algebra of H -invariant regular functions on Z has a G -invariant filtration such that the associated graded algebra is the algebra of regular functions of some explicit horospherical subgroup of G . The deformation method in its usual form, as developed...

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