Invarianten unipotenter Gruppen.
Invariants de plusieurs formes binaires
Invariants d'un sous-groupe unipotent maximal d'un groupe semi-simple
Soit un groupe algébrique semi-simple complexe, un sous-groupe unipotent maximal de , un tore maximal de normalisant . Si est un -module rationnel de dimension finie, alors opère sur l’algèbre des fonctions polynomiales sur ; la structure de -module de est décrite par la -algèbre des -invariants de . Cette algèbre est de type fini et multigraduée (par le degré de et le poids par rapport à ). On donne une formule intégrale pour la série de Poincaré de cette algèbre graduée....
Invariants of four subspaces
We consider problems in invariant theory related to the classification of four vector subspaces of an -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.
Invariants of several matrices.
Invariants of Unipotent Radicals.
Lifting mappings over invariants of finite groups.
Linear bounds for levels of stable rationality
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 for Vectorbundles on Pn(C).
Moduli of representations of the fundamental group of a smooth projective variety I
Moduli spaces of local systems and higher Teichmüller theory
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...
Monodromy of the hypergeometric differential equation of type (3,6) II. The unitary reflection group of order
Noether's problem over an algebraically closed field.
On classical invariant theory and binary cubics
Let be a reductive complex algebraic group, and let denote the algebra of invariant polynomial functions on the direct sum of copies of the representations space of . There is a smallest integer such that generators and relations of can be obtained from those of by polarization and restitution for all . We bound and the degrees of generators and relations of , extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics.
On complete orbit spaces of SL(2) actions
On deformation method in invariant theory
In this paper we relate the deformation method in invariant theory to spherical subgroups. Let be a reductive group, an affine -variety and a spherical subgroup. We show that whenever is affine and its semigroup of weights is saturated, the algebra of -invariant regular functions on has a -invariant filtration such that the associated graded algebra is the algebra of regular functions of some explicit horospherical subgroup of . The deformation method in its usual form, as developed...
On finite same-invariant linear groups.
On invariants of a set of matrices.
On normal representations of G-actions on projective varieties.
On representations of with algebras of invariants being complete intersections.