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The Projective Geometry of Freudenthal's Magic Square

The projective geometry of Freudenthal's magic square.

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 May 2001Embargo end date: 01 Jan 1999 English Publisher:Elsevier BVJournal:Journal of Algebra, volume 239, pages 477-512 (issn: 0021-8693,

Authors: Joseph M. Landsberg; Joseph M. Landsberg; Laurent Manivel; Laurent Manivel;

doi: 10.1006/jabr.2000.8697 , 10.48550/arxiv.math/9908039

arXiv: http://arxiv.org/abs/math/9908039

The Projective Geometry of Freudenthal's Magic Square

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Abstract

We connect the algebraic geometry and representation theory associated to Freudenthal's magic square. We give unified geometric descriptions of several classes of orbit closures, describing their hyperplane sections and desingularizations, and interpreting them in terms of composition algebras. In particular, we show how a class of invariant quartic polynomials can be viewed as generalizations of the classical discriminant of a cubic polynomial.

30 pages, LaTeX2e

Related Organizations

Grenoble Alpes University
France
Centre national de la recherche scientifique
France
Georgia Institute of Technology
United States

Keywords

Mathematics - Differential Geometry, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Algebra and Number Theory, Noncommutative Jordan algebras, Classical problems, Schubert calculus, Composition algebras, Mathematics - Algebraic Geometry, Differential Geometry (math.DG), FOS: Mathematics, Representation Theory (math.RT), Classical groups (algebro-geometric aspects), Algebraic Geometry (math.AG), Mathematics - Representation Theory

2dim

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Top 10%

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