Displaying similar documents to “On classical invariant theory and binary cubics”

Constructive invariant theory for tori

David Wehlau (1993)

Annales de l'institut Fourier

Similarity:

Consider a rational representation of an algebraic torus T on a vector space V . Suppose that { f 1 , ⋯ , f p } is a homogeneous minimal generating set for the ring of invariants, k [ V ] T . New upper bounds are derived for the number N V , T : = max { deg f i } . These bounds are expressed in terms of the volume of the convex hull of the weights of V and other geometric data. Also an algorithm is described for constructing an (essentially unique) partial set of generators { f 1 , ⋯ , f s } consisting of monomials and such that k [ V ] T is integral over k [ f 1 , ⋯ , f s ] . ...

Invariants of four subspaces

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

Annales de l'institut Fourier

Similarity:

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.

On deformation method in invariant theory

Dmitri Panyushev (1997)

Annales de l'institut Fourier

Similarity:

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,...

S L 2 , the cubic and the quartic

Yannis Y. Papageorgiou (1998)

Annales de l'institut Fourier

Similarity:

We describe the branching rule from S p 4 to S L 2 , where the latter is embedded via its action on binary cubic forms. We obtain both a numerical multiplicity formula, as well as a minimal system of generators for the geometric realization of the rule.