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The projective geometry of Freudenthal’s magic square. (English) Zbl 1064.14053
Summary: 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.

MSC:
14L35 Classical groups (algebro-geometric aspects)
14N15 Classical problems, Schubert calculus
17A15 Noncommutative Jordan algebras
17A75 Composition algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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