Chevalley groups of type \(E_7\) in the 56-dimensional representation.

DOI10.1007/s10958-011-0641-yzbMath1306.20050OpenAlexW2041134079MaRDI QIDQ476673

A. Yu. Luzgarev, Nikolai A. Vavilov

Publication date: 2 December 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-011-0641-y

zbMATH Keywords

minimal representationsChevalley groups over commutative ringsminimal modules

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (7)

Computers as a novel mathematical reality. I: A personal account ⋮ Minuscule Schubert varieties of exceptional type ⋮ Calculations in exceptional groups over rings. ⋮ Decomposition of unipotents for \(\mathrm{E}_6\) and \(\mathrm{E}_7\): 25 years after ⋮ Calculations in exceptional groups, an update. ⋮ Normalizer of the Chevalley group of type ${\operatorname E}_7$ ⋮ ${\mathrm A}_3$-proof of structure theorems for Chevalley groups of types ${\mathrm E}_6$ and ${\mathrm E}_7$ II. Main lemma

Cites Work

• Fourth-degree invariants for \(G(\mathrm E_7,R)\) not depending on the characteristic.
• The Tits indices over semilocal rings.
• Some more exceptional numerology.
• Identification of matrix generators of a Chevalley group.
• Quantum cohomology of minuscule homogeneous spaces
• Localization-completion strikes again: relative \(K_1\) is nilpotent by Abelian
• Oktaven, Ausnahmegruppen und Oktavengeometrie
• Some multilinear forms with large isometry groups
• Some representations of exceptional Lie algebras
• On the classification of Freudenthal triple systems and Lie algebras of type \(E_7\)
• The conjugate classes of unipotent elements of the Chevalley groups \(E_ 7\) and \(E_ 8\).
• Basic representations of affine Lie algebras and dual resonance models
• Surjective stability for the \(K_ 1\)-functor for some exponential Chevalley groups
• On the stability of the \(K_1\)-functor for Chevalley groups of type \(E_7\)
• Isotropic trialitarian algebraic groups
• Embeddings of \(U_ 3(8)\), \(Sz(8)\) and the Rudvalis group in algebraic groups of type \(E_ 7\)
• Kostant's conjecture holds for \(E_ 7\): \(L_ 2(37)<E_ 7(\mathbb{C})\)
• Embeddings and hyperplanes of the Lie incidence geometry of type \(E_{7,1}\)
• The kernel of the Rost invariant, Serre's conjecture II and the Hasse principle for quasi-split groups \(^{3,6}D_4\), \(E_6\), \(E_7\).
• Explicit Cayley triples in real forms of \(E_ 7\).
• Homology of the double and the triple loop spaces of \(E_6\), \(E_7\) and \(E_8\)
• Projective geometry of Freudenthal's varieties of certain type
• On the structure of parabolic subgroups in algebraic groups
• Chevalley groups over commutative rings. I: Elementary calculations
• A characterization of quadratic forms of type \(E_6\), \(E_7\), and \(E_8\)
• A third look at weight diagrams
• The fifty-six-dimensional module for \(E_ 7\). I: A four form for \(E_ 7\)
• Configurations of seven lines on the real projective plane and the root system of type \(E_7\)
• Parabolic subgroups with Abelian unipotent radical
• Relative commutator calculus in Chevalley groups.
• A minimal representation for the Lie algebra \(E_ 7\)
• Chevalley groups over local rings
• GROUPS OF TYPEE₇OVER ARBITRARY FIELDS
• The closure diagram for nilpotent orbits of the split real form of 𝐸₇
• Elementary subgroup of an isotropic reductive group is perfect
• Normalizer of the Chevalley group of type ${\mathrm E}_6$
• Elementary subgroups of isotropic reductive groups
• Moufang quadrangles of type E 6 and E 7
• Relative subgroups in Chevalley groups
• Normal Structure of Maximal Parabolic Subgroups in Chevalley Groups over Rings
• Whitehead groups of chevalley groups over polynomial rings
• A System of Quadrics Describing the Orbit of the Highest Weight Vector
• Exceptional Lie Algebras and Related Algebraic and Geometric Structures
• Minimal representations of E6, E7, and E8 and the generalized Capelli identity.
• Contracting modules and standard monomial theory for symmetrizable Kac-Moody algebras
• HS <E ₇ (5)
• The octonions
• Chevalley groups of type E7 in the 56-dimensional representation
• Visual Basic Representations
• Computing in groups of Lie type
• On standard L-functions for E6 and E7.
• On the lattice of subgroups of chevalley groups containing a split maximal torus
• AN A₃-PROOF OF STRUCTURE THEOREMS FOR CHEVALLEY GROUPS OF TYPES E₆ AND E₇
• The $({\bf A_2,G_2})$ duality in ${\bf E_6}$, octonions and the triality principle
• Some Groups of Type E₇
• Zero Cycles on a Twisted Cayley Plane
• Les nombres de Tamagawa de certains groupes exceptionnels
• A NEW TYPE OF NON ASSOCIATIVE ALGEBRAS
• Groups of type E7.
• Some Irreducible Representations of Exceptional Algebraic Groups
• A Geometry for E 7
• Generators, Relations and Coverings of Chevalley Groups Over Commutative Rings
• Strictly Regular Elements in Freudenthal Triple Systems
• Sur les sous-groupes arithmétiques des groupes semi-simples déployés
• Unramified cohomology of classifying varieties for exceptional simply connected groups
• On the structure of parabolic subgroups
• On normal subgroups of Chevalley groups over commutative rings
• On normal subgroups of Chevalley groups over commutative rings
• Constructions for octonion and exceptional Jordan algebras
• Matrix generators for exceptional groups of Lie type
• The projective geometry of Freudenthal's magic square.
• On simply laced Lie algebras and their minuscule representations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Chevalley groups of type \(E_7\) in the 56-dimensional representation.