SIMPLE GROUPS STABILIZING POLYNOMIALS

DOI10.1017/fmp.2015.3zbMath1365.20046arXiv1309.6611OpenAlexW2120779243MaRDI QIDQ2941124

Robert M. Guralnick, Skip Garibaldi

Publication date: 27 August 2015

Published in: Forum of Mathematics, Pi (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.6611

zbMATH Keywords

irreducible representationsimple algebraic groupexceptional group \(E_{8}\)

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Representation theory for linear algebraic groups (20G05) Vector and tensor algebra, theory of invariants (15A72) Exceptional groups (20G41)

Related Items

Freudenthal duality in gravity: from groups of type \(E_{7}\) to pre-homogeneous spaces ⋮ Non-associative Frobenius algebras for simply laced Chevalley groups ⋮ Essential dimension of algebraic groups, including bad characteristic ⋮ Generically free representations. II: Irreducible representations ⋮ Generically free representations. III: Extremely bad characteristic ⋮ Notes on \(G_2\): the Lie algebra and the Lie group ⋮ Spinors and essential dimension ⋮ Overgroups of exterior powers of an elementary group. levels ⋮ Topological generation of special linear groups ⋮ Simple Lie groups stabilizing \(G\)-invariant norms ⋮ A class of continuous non-associative algebras arising from algebraic groups including ⋮ Relations in quantized function algebras ⋮ Supersymmetry and the Suzuki chain ⋮ On the realizability of group actions ⋮ Calculations in exceptional groups, an update. ⋮ $E_8$, the most exceptional group ⋮ Generic stabilizers for simple algebraic groups ⋮ The moduli space of marked generalized cusps in real projective manifolds

Cites Work

• Fourth-degree invariants for \(G(\mathrm E_7,R)\) not depending on the characteristic.
• Non-parabolic prehomogeneous vector spaces and exceptional Lie algebras
• Vinberg's \(\theta \)-groups in positive characteristic and Kostant-Weierstrass slices
• Homomorphismes abstraits de groupes algébriques simples
• Automorphisms of classical Lie algebras
• Die adjungierten Darstellungen der Chevalley-Gruppen
• Alternating forms and self-adjoint operators
• Some remarks on nilpotent orbits
• Buildings of spherical type and finite BN-pairs
• Geometric reductivity over arbitrary base
• Representations of simple Lie groups with regular rings of invariants
• Automorphismes et déformations des variétés de Borel
• On a linear structure of the quotient variety by a finite reflexion group
• Modules for algebraic groups with finitely many orbits on subspaces
• The finite irreducible linear groups with polynomial ring of invariants
• Automorphism groups of finite dimensional simple algebras.
• Freudenthal triple systems by root system methods
• Essential dimension of algebraic groups and integral representations of Weyl groups
• \(\text{GL}(4)\)-orbits in a \(16\)-dimensional module for characteristic \(3\)
• Conjugacy classes of n-tuples in Lie algebras and algebraic groups
• Reductive subgroups of reductive groups in nonzero characteristic.
• Composition algebras and cyclic \(p\)-algebras in characteristic 3
• A geometric approach to complete reducibility.
• Classifying forms of simple groups via their invariant polynomials
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Troisième partie). Rédigé avec la colloboration de J. Dieudonné
• Groupes reductifs
• Complements à l'article: Groupes reductifs
• Invariants symétriques entiers des groupes de Weyl et torsion
• Sur une généralisation du groupe orthogonal à quatre variables
• Geometric Complexity Theory I: An Approach to thePvs.NPand Related Problems
• Quaternion Algebras with the Same Subfields
• INVARIANTS OF FINITE GROUP SCHEMES
• Linear preservers and representations with a 1-dimensional ring of invariants
• Representations of Algebraic Groups
• Some Basic Theorems on Algebraic Groups
• The octic E8 invariant
• Linear maps preserving invariants
• LIE ALGEBRAS WITHOUT STRONG DEGENERATION
• The Affine Permutation Groups of Rank Three
• Basic sets of invariant polynomials for finite reflection groups
• On a certain generator system of the ring of invariants of a finite reflection group
• SIMPLE ALGEBRAS AND QUADRATIC FORMS
• A classification of irreducible prehomogeneous vector spaces and their relative invariants
• Affine Coset Spaces of Reductive Algebraic Groups
• THE WEYL GROUP OF A GRADED LIE ALGEBRA
• Pythagoras numbers of fields
• Small Degree Representations of Finite Chevalley Groups in Defining Characteristic
• Flat bases of invariant polynomials and P̂-matrices of E7 and E8
• Division algebras with infinite genus
• A Classification of Spinors Up to Dimension Twelve
• DEFORMATIONS OF SIMPLE LIE ALGEBRAS
• The Exceptional Simple Lie Algebras F ₄ and E ₆
• On the structure of parabolic subgroups
• On simply laced Lie algebras and their minuscule representations
• Fields of \(u\)-invariant \(9\)
• Unnamed Item